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THE 


PAEADISE  OF  CHILDHOOD: 


A  MANUAL  FOR  SELF  INSTRUCTION  IN  FRIEDRICH  FROEBEL'S 
EDUOATIONAL  PRINCIPLES, 


AND  A  PRACTICAI. 


Gruide  to  Kinder-Gartners. 


BT 


EDWARD    IWIEBE. 


WITH   SETEKTY-FOUE  PLATES   OF  ILLUSTRATIONS. 


MILTON  BRADLEY  &  COMPANY, 

SPRINGFIELD,  MASS. 


mOMlOS  IlfiH. 


Entered  according  to  Act  of  Congress,  in  the  year  1869,  by 

MILTON   BRADI.FY   &   COMPANY, 

In  the  Clerk's  Office  of  the  District  Court  of  the  District  of  Massachusetts. 


SPRINGFIELD  PRINTING  COMPANY, 

ELBCTROTYPERS,    PRINTERS  AND   BINDERS, 

SPRINGFIELD,   MASS. 


INTRODUCTION. 


Until  a  recent  period,  but  little  interest  has  been 
tit  by  people  in  this  country,  with  regard  to  the 
Kinder-Garten  method  of  instruction,  for  the  simple 
reason  that  a  correct  knowledge  of  the  system  has 
never  been  fully  promulgated  here.  However  the  lec- 
tures of  Miss  E.  P.  Peabody  of  Cambridge,  Mass., 
have  awakened  some  degree  of  enthusiasm  upon  the 
subject  in  different  localities,  and  the  establishment 
of  a  few  Kinder-Garten  schools  has  served  to  call  forth 
a  more  general  inquiry  concerning  its  merits. 

We  claim  that  every  one  who  believes  in  rational 
education,  will  become  deeply  interested  in  the  pecu- 
liar features  of  the  work,  after  having  become  ac- 
quainted with  Froeoel's  principles  and  plan;  and 
that  all  that  is  needed  to  enlist  tne  popular  sentiment 
in  its  favor  is  the  establishment  of  institutions  of  this 
kind,  in  this  country,  upon  the  right  basis. 

With  such  an  object  in  view,  we  propose  to  present 
an  outline  of  the  Kinder-Garten  plan  as  developed  by 
its  originator  in  Germany,  and  to  a  considerable  ex- 
tent by  his  followers  in  France  and. England. 

But  as  Froebel's  is  a  system  which  must  be  carried 
out  faithfully  in  all  its  important  features,  to  insure 
success,  we  must  adopt  his  plan  as  a  whole  and  carry 
it  out  with  such  modifications  of  secondary  minutiae 
only,  as  the  individual  case  may  acquire  without  vio- 
lating its  fundamental  principles.  If  this  cannot  be 
accomplished,  it  were  better  not  to  attempt  the  task 
at  all. 

The  present  work  is  entitled  a  Manual  for  Self- 
tnstrudion  and  a  p7-actical  Guide  for  Kinder-Gartners. 
Those  who  design  to  Use  it  for  either  of  these  pur- 
poses, must  not  eX])ect  to  find  in  it  all  that  they  ought  to 


know  in  order  to  instruct  the  young  successfully  ac- 
cording to  Froebel's  principles.  No  book  can  evef 
be  written  which  is  able  to  make  a  perfect  Kinder- 
Gartner  ;  this  requires  the  training  of  an  able  teacher 
actively  engaged  in  the  work  at  the  moment 
"Kinder-Garten  Culture,"  says  Miss  Peabody,  in  the. 
preface  to  her  "Moral  Culture  of  Infancy,"  "is  the 
adult  mind  entering  into  the  child's  world  and  ap- 
preciating nature's  intention  as  displayed  in  every 
impulse  of  spontaneous  life,  so  directing  it  that  the 
joy  of  success  may  be  ensured  at  every  step,  and 
artistic  things  be  actually  pioduced.  which  gives  the 
self  reliance  and  conscious  intelligence  that  ought  to 
discriminate  human  power  from  bima  force." 

With  this  thought  constantly  present  in  his  mind, 
the  reader  will  find,  in  this  book,  all  that  is  indispens- 
ably necessary  for  him  to  know,  from  the  first  estab- 
lishment of  the  Kinder-Garten  through  all  its  various 
degrees  of  development,  including  the  use  of  the  mate- 
rials and  the  engagement  in  such  occupations  as  are 
peculiar  to  the  system.  There  is  much  more,  hovr- 
e^er,  that  can  be  learned  only  by  individual  obser- 
vation. The  fact,  that  here  and  there,  persons,  pre- 
suming upon  the  slight  knowledge  which  they  may 
have  gained  of  Froebel  and  his  educational  principles, 
from  books,  have  established  schools  called  Kinder- 
Gartens,  which  in  reality  had  nothing  in  common  with 
the  legitimate  Kinder-Garten  but  the  name,  has  caused 
distrust  and  even  opposition,  in  many  minds  towards 
everything  that  pertains  to  this  method  of  instruc- 
tion. In  discriminating  between  the  spurious  and  the 
real,  as  is  the  design  of  this  work,  the  author  would 
mention  with  spcti.il  cf>mmendation,  the  Educational 


iSi750310 


IV 


INTRODUCTION. 


Institute  conducted  by  Mrs.  and  Aiiss  Kricge  in 
Boston.  It  connects  with  the  Kinder-Garten  proper, 
a  Training  School  for  ladies,  and  any  one  who  wishes 
to  be  instructed  in  the  correct  method,  will  there  be 
able  to  acquire  the  desired  knowledge. 

Besides  the  Institute  just  mentioned,  there  is  one 
in  Springfield,  Mass.,  under  the  supervision  of  the 
writer,  designed  not  only  for  the  instruction  of  classes 
of  children  in  accordance  with  these  principles,  but 
also  for  imparting  information  to  those  who  are  de- 
sirous to  become  Kinder-Gartners.  From  this  source, 
the  method  has  already  been  acquired  in  several  in- 
stances, and  as  one  result,  it  has  been  introduced  into 
two  of  the  schools  connected  with  the  State  Institu- 
tion at  Monson,  Mass. 

The  writer  was  in  early  life  acquainted  with  Froebel ; 
and  his  subsequent  experience  as  a  teacher  has  only 
served  to  confirm  the  favorable  opinion  of  the  system, 
which  he  then  derived  from  a  personal  knowledge  of 


its  inventor.  A  desire  to  promote  the  interests  of  true 
education,  has  led  him  to  undertake  this  work  of  inter- 
pretation and  explanation. 

Without  claiming  for  it  perfection,  he  believes  that, 
as  a  guide,  it  will  stand  favorably  in  comparison  with 
any  publication  upon  the  subject  in  the  English  or  the 
French  language. 

The  German  of  Marenholtz,  Goldammer,  Morgen- 
stern  and  Froebel  have  been  made  use  of  in  its  prep- 
aration, and  though  new  features  have,  in  rare  cases 
only,  been  added  to  the  original  plan,  several  changes 
have  been  made  in  minor  details,  so  as  to  adapt  this 
mode  of  instruction  more  readily  to  the  American 
mind.  This  has  been  done,  however,  without  omit- 
ting aught  of  that  German  thoroughness,  which  char- 
acterizes so  strongly  every  feature  of  Froebel's  system. 

The  plates  accompanying  this  work  are  reprints 
from  "  Goldammer's  Kinder-Garten,".a  book  recently 
published  in  Germany. 


PARENTS  ASSOCIATION  OF  THE 
BERKELEY  ELEMENTARY  SCHOOL 


The   Paradise  of  Childhood  : 
A  GUIDE  TO  KINDER-GARTNERS 


ESTABLISHMENT  OF  A  KINDER-GARTEN. 


The  requisites  for  the  establishment  of  a 
"  Kinder  Garten  "  are  the  following  : 

1.  A  house,  containing  at  least  one  large 
room,  spacious  enough  to  allow  the  children, 
not  only  to  engage  in  all  their  occupations, 
both  sitting  and  standing,  but  also  to  practice 
their  movement  plays,  which,  during  inclem- 
ent seasons,  must  be  done  in-doors. 

2.  Adjoining  the  large  room,  one  or  two 
smaller  rooms  for  sundry  purposes. 

3.  A  number  of  tables,  according  to  the 
size  of  ■  the  school,  each  table  affording  a 
smooth  surface  ten  feet  long  and  four  feet 
wide,  resting  on  movable  frames  from  eighteen 
to  twenty-four  inches  high.  The  table  should 
be  divided  into  ten  equal  squares,  to  accom- 
modate as  many  pupils ;  and  each  square 
subdivided  into  smaller  squares  of  one  inch, 
to  guide  the  children  in  many  of  their  occu- 
pations. On  either  side  of  the  tables  should 
be  settees  with  folding  seats,  or  small  chairs 
ten  to  fifteen  inches  high.  The  tables  and 
settees  should  not  be  fastened  to  the  floor,  as 
they  will  need  to  be  removed  at  times  to 
make  room  for  occupations  in  which  they  are 
not  used. 

4.  A  piano-forte  for  g)'mnastic  and  musical 
exercises — the  latter  being  an  important  feat- 
ure of  the  plan,  since  all  the  occupations  are 
interspersed  with,  and  many  of  them  accom- 
panied by,  singing. 

5.  Various  closets  for  keeping  the  apparatus 
and  work  of  the  children — a  wardrobe,  wash- 
stand,  chairs,  teacher's  table,  &c. 


The  house  should  be  pleasantly  located, 
removed  from  the  bustle  of  a  thoroughfare, 
and  its  rooms  arranged  with  strict  regard  to 
hygienic  principles.  A  garden  should  sur- 
round or,  at  least,  adjoin  the  building,  for 
frequent  out  door  exercises,  and  for  gardening 
purposes.  A  small  plot  is  assigned  to  each 
child,  in  which  he  sows  the  seeds  and  culti- 
vates the  plants,  receiving,  in  due  time,  the 
flowers  or  fruits,  as  the  result  of  his  industry 
and  care. 

When  a  Training  School  is  connected  with 
the  Kinder-Garten  the  children  of  the  "  Gar- 
ten" are  divided  into  groups  of  five  or  ten — 
each  group  being  assisted  in  its  occupations 
by  one  of  the  lady  pupils  attending  the  Train- 
ing School. 

Should  there  be  a  greater  number  of  such 
assistants  than  can  be  conveniently  occupied 
in  the  Kinder  Garten,  they  may  take  turns 
with  each  other.  In  a  Training  School  of 
this  kind,  under  the  charge  of  a  competent 
director,  ladies  are  enabled  to  acquire  a  thor- 
ough and  practical  knowledge  of  the  system. 
They  should  bind  themselves,  however,  10 
remain  connected  with  the  inj^titution  a  spti  i- 
fied  time,  and  to  follow  out  the  details  of  tl  c 
method  patiently,  if  they  aim  to  fit  themselves 
to  conduct  a  Kinder-Garten  with  success. 

In  any  establishment  of  more  than  twenty 
children,  a  nurse  should  be  in  constant  at- 
tendance. It  should  be  her  duty  also  to 
preserve  order  and  cleanliness  in  the  rooms, 
and  to  act  as  janitrix  to  the  institution. 


MEANS    AND    WAYS    OF   OCCUPATION 

IN    THE    KINDER-GARTEN. 


Before  entering  into  a  description  of  the 
various  means  of  occupation  in  the  Kinder- 
Garten,  it  will  be  proper  to  state  that  Fried- 
rich  Froebel,  the  inventor  of  this  system  of 
education,  calls  all  occupations  in  the  Kinder- 
Garten  "//a^j,"  and  the  materials  for  occupa- 
tion "^^jr."  In  these  systematically-arranged 
plays,  Froebel  starts  from  the  fundamental 
idea  that  all  education  should  begin  with  a 
development  of  the  desire  for  activity  innate 
in  tlis  child ;  and  he  has  been,  as  is  universally 
acknowledged,  eminently  successful  in  this 
part  of  his  important  work.  Each  step  in 
the  course  of  training  is  a  logical  sequence 
of  the  preceding  one ;  and  the  various  means 
of  occupation  are  developed,  one  from  another, 
in  a  perfectly  natural  order,  beginning  with  the 
simplest  and  concluding  with  the  most  difficult 
features  in  all  the  varieties  of  occupation.  To- 
gether, they  satisfy  all  the  demands  of  the  child's 
nature  in  respect  both  to  mental  and  physical 
culture,  and  lay  the  surest  foundation  for  all 
subsequent  education  in  school  and  in  life. 

The  tint:  of  occupation  in  the  Kinder-Garten 
is  three  or  four  hours  on  each  week  day,  usually 
from  9  to  1 2  or  I  o'clock  ;  and  the  time  allot- 
ted to  each  separate  occupation,  including  the 
changes  from  one  to  another,  is  from  twenty  to 
thirty  minutes.  Move7nent  plays,  so-called,  in 
which  the  children  imitate  the  flying  of  birds, 
swimming  of  fish,  the  motions  of  sowing,  mow- 
wing,  threshing,  &c.,  in  connection  with  light 
gymnastics  and  vocal  exercises,  alternate  with 
the  plays  performed  in  a  sitting  posture.  All 
occupations  that  can  be  engaged  in  out  of 
doors,  are  carried  on  in  the  garden  whenever 
the  season  and  weather  permit. 


For  the  reason  that  the  various  occupations, 
as  previously  stated,  are  so  intimately  con- 
nected, growing,  as  it  were,  out  of  each  other, 
they  are  introduced  very  gradually,  so  as  to 
afford  each  child  ample  time  to  become  suffi- 
ciently prepared  for  the  next  step,  without 
interfering,  however,  with  the  rapid  progress 
of  such  as  are  of  a  more  advanced  age,  or 
endowed  with  stronger  or  better  developed 
faculties. 

The  following  is  a  list  of  the  gifts  or  ma- 
terial and  means  of  occupation  in  the  Kinder- 
Garten,  each  of  which  will  be  specified  and 
described  separately  hereafter. 

There  are  altogether  twenty  gifts,  according 
to  Froebel's  general  definition  of  the  term,  al- 
though the  first  six  only  are  usually  designated 
by  this  name.  We  choose  to  follow  the  classi- 
fication and  nomenclature  of  the  great  inventor 
of  the  system. 

LIST   OF   FROEBEL'S   GIFTS. 

1.  Six  rubber  balls,  covered  with  a  net-work 
of  twine  or  worsted  of  various  colors- 

2 .  Sphere,  cube,  and  cylinder,  made  of  wood. 

3.  Large  cube,  consisting  of  eight  small 
cubes. 

4.  Large  cube,  consisting  of  eight  oblong 
parts. 

5.  Large  cube,  consisting  of  'i^hole,  half, 
and  quarter  tubes. 

6.  Large  cube,  consisting  of  doubly  divided 
oblongs. 

[The  third,  fourth,  fifth  and  sixth  gifts  serve 
for  building  purposes.] 

7.  Square  and  triangular  tablets  for  laying 
of  figures. 


GUIDE   TO    KINDER-GaRTNERS. 


8.  Staffs  for  laying  of  figures. 

9.  Whole    and    halt    rings   for   laying   of 
figures. 

10.  Material  for  drawing. 

11.  Material  for  perforating. 

12.  Material  for  embroidering. 

13.  Material  for  cutting  of  paper  and  com- 
bining pieces. 


14.  Material  for  braiding. 

15.  Slats  for  interlacing 

16.  The  slat  with  many  links. 

17.  Material  for  intertwining. 

18.  Material  for  paper  folding. 

19.  Material  for  peas-work. 

20.  Material  for  modeling. 


THE    FIRST    GIFT. 


The  First  Gift,  which  consists  of  six  rubber 
balls,  over- wrought  with  worsted,  for  the  pur- 
pose of  representing  the  three  fundamental 
and  three  mixed  colors,  is  introduced  in  this 
manner: 

The  children  are  made  to  stand  in  one  or 
two  rows,  with  heads  erect,  and  feet  upon  a 
given  line,  or  spots  marked  on  the  floor. 
The  teacher  then  gives  directions  like  the 
following : 

"  Lift  up  your  right  hands  as  high  as  you 
can  raise  them." 

"Take  them  down." 

"  Lift  up  your  left  hands."     "  Down." 

"  Lift  up  both  your  hands."     "  Down." 

"  Stretch  forward  your  right  hands,  that  I 
may  give  each  of  you  something  that  I  have 
in  my  box." 

The  teacher  then  places  a  ball  in  the  hand 
of  each  child,  and  asks — 

"  Who  can  tell  me  the  name  of  what  you 
have  received .?  "  Questions  may  follow  about 
the  color,  material,  shape,  and  other  qualities 
of  the  bail,  which  will  call  forth  the  replies, 
blue,  yellouK  rubber,  round,  light,  soft,  &c. 

The  children  are  then  required  to  repeat 
sentences  pronounced  by  the  teacher,  as — 
"The  ball  is  round;"  ''My  ball  is  green;'' 
''All  these  balls  are  made  of  rubber,"  &c. 
They  are  then  required  to  return  all,  except 
the  blue  balls,  those  who  give  up  theirs  being 
allowed  to  select  from  the  box  a  blue  ball  in 


exchange  ;  so  that  in  the  end  each  child  has 
a  ball  of  that  color.  The  teacher  then  says  : 
"  Each  of  you  has  now  a  blue,  rubber  ball. 
which  is  roimd.  j-*?/?,  and  light ;  and  these  balls 
will  be  your  balls  to  play  with.  I  will  give 
you  another  ball  to-morrow,  and  the  next  day 
another,  and  so  on,  until  you  have  quite  a 
number  of  balls,  all  of  which  will  be  of  rub- 
ber, but  no  two  of  the- same  color." 

The  six  differently  colored  balls  are  to  be 
used,  one  on  each  day  of  the  week,  which 
assists  the  children  in  recollecting  the  days  of 
the  week,  and  the  colors.  After  distributing 
the  balls,  the  same  questions  may  be  asked  as 
at  the  beginning,  and  the  children  taught  to 
raise  and  drop  their  hands  with  the  balls  in 
them  ;  and  if  there  is  time,  they  may  make  a 
few  attempts  to  throw  and  catch  the  balls. 
This  is  enough  for  the  first  lesson  ;  and  it  will 
be  sure  to  awaken  enthusiasm  and  delight  in 
the  children. 

The  object  of  the  first  occupation  is  to  teach 
the  children  to  distinguish  between  the  right 
and  the  left  hand,  and  to  name  the  various 
colors.  It  may  serve  also  to  develop  their 
vocal  organs,  and  instruct  them  in  the  rules 
of  politeness.  How  the  latter  may  be  accom- 
plished, even  with  such  simple  occupation  as 
playing  with  balls,  may  be  seen  from  the  fol- 
lowing : 

In  presenting  the  balls,  pains  should  be 
taken  to  make  each   child  extend  the  right 


GUIDE    TO    KINDER-GARTNERS. 


hand,  and  do  it  gracefully.  The  teacher,  in 
putting  the  ball  into  the  little  outstretched 
hand,  says : 

"  Charles,  I  place  this  red  (green,  yellow, 
&c.,)  ball  into  your  right  hand."  The  child 
is  taught  to  reply — 

"  I  thank  you,  sir." 
After  the  play  is  over,  and  the  balls  are  to 
be  replaced,  each  one  says,  in  re^turning  his 
ball— 

"  I  place  this  red  (green,  yellow,  &c.,)  ball, 
with  my  right  hand,  into  the  box," 

When  the  children  have  acquired  some 
knowledge  of  the  different  colors,  they  may 
be  asked  at  the  commencement : 

"  With  which  ball  would  you  like  to  play 
this  morning — the  green,  red,  or  blue  one  ? " 
The  child  will  reply: 

"  With  the  blue  one,  if  you  please  ;"  or  one 
of  such  other  color  as  may  be  preferred. 

It  may  appear  rather  monotonous  to  some 
to  have  each  child  repeat  the  same  phrase  ; 
but  it  is  only  by  constant  repetition  and 
patient  drill  that  anything  can  be  learned 
accurately ;  and  it  is  certainly  important  that 
these  youthful  minds,  in  their  formative  state, 
should  be  taught  at  once  the  beauty  of  order 
and  the  necessity  of  rules.  So  the  left  hand 
should  never  be  employed  when  the  right 
hand  is  required ;  and  all  mistakes  should 
be  carefully  noticed  and  corrected  by  the 
teacher.  One  important  feature  of  this  sys- 
tem is  the  inculcation  of  habits  of  precision. 

The  children's  knowledge  of  color  may  be 
improved  by  asking  them  what  other  things 
are  similar  to  the  different  balls,  in  respect  to 
color.  After  naming  several  objects,  they 
may  be  made  to  repeat  sentences  like  the  fol- 
lowing : 

'•  My  ball  is  green,  like  a  leaf"  "  My  ball 
is  yellow,  like  a  lemon."  "  And  mine  is  red, 
like  blood,"  &c. 

Whatever  is  pronounced  in  these  conversa- 
tional lessons  should  be  articulated  very  dis- 
tinctly and  accurately,  so  as  to  develop  the 
organs  of  speech,  and  to  correct  any  defect 
of  utterance,  whether  constitutional   or   the 


result  of  neglect.  Opportunities  ior  pl.ci.ctic 
and  elocutionary  practice  are  here  afforded. 
Let  no  one  consider  the  infant  period  as  too 
early  for  such  exercises.  If  children  learn  to 
speak  well  before  they  learn  to  read,  they 
never  need  special  instruction  in  the  art  of 
reading  with  expression. 

For  a  second  play  with  the  balls,  the  class 
forms  a  circle,  after  the  children  have  received 
the  balls  in  the  usual  manner.  They  need  to 
stand  far  enough  apart,  so  that  each,  with 
arms  extended,  can  just  touch  his  neighbor's 
hand.  Standing  in  this  position,  and  having 
the  balls  in  their  right  hands,  the  children 
pass  them  into  the  left  hands  of  their  neigh- 
bors. In  this  way,  each  one  gives  and  re- 
ceives a  ball  at  the  same  time,  and  the  left 
hands  should,  therefore,  be  held  in  such  a 
manner  that  the  balls  can  be  readily  placed 
in  them.  The  arms  are  then  raised  over  the 
head,  and  the  balls  passed  from,  the  left  into 
the  right  hand,  and  the  arms  again  extended 
into  the  first  position.  This  process  is  re- 
peated until  the  balls  make  the  complete 
circuit,  and  return  into  the  right  hands  of  the 
original  owners.  The  balls  are  then  passed 
to  the  left  in  the  srmc  way,  everything  being 
done  in  an  opposite  direction.  This  exercise 
should  be  continued  until  it  can  be  done 
rapidly  and,  at  the  same  time,  gracefully. 

Simple  as  this  performance  may  appear  to 
those  who  have  never  tried  it,  it  is,  neverthe- 
less, not  easily  done  by  very  young  children 
without  frequent  mistakes  and  interruptions. 
It  is  better  that  the  children  should  not  turn 
their  heads,  so  as  to  watch  their  hands  during 
the  changes,  but  be  guided  solely  by  the  sense 
of  touch  ;  and  to  accomplish  this  with  more 
certainty,  they  may  be  required  to  close  thar 
eyes.  It  is  advisr.ble  rot  to  introduce  this 
play  or  anv  of  the  following,  until  expertr.css 
is  acquired  in  the  first  and  simpler  form. 

In  the  third  play,  the  children  form  in  two 
rows  fronting  each  other.  Those  of  one  rcw 
only  receive  balls.  These  they  toss  to  the 
opposite  row  :  first,  one  by  one  ;  the*  two  by 
two;  finally,  the  whole  row  at  once,  always 


GUIDE    TO    KINDER-GARTNERS. 


to  the  counting  of  the  teacher — "one,  two, 
throw.'' 

Again,  forming  four  rows,  the  children  in 
the  first  row  toss  up  and  catch,  then  throw  to 
the  second  row,  then  to  the  third,  then  to  the 
fourth,  accompanying  the  exercise  with  count- 
ing as  before,  or  with  singing,  as  soon  as  this 
can  be  done.  * 

For  a  further  variety,  the  balls  are  thrown 
upon  the  floor,  and  caught,  as  they  rebound, 
with  the  right  hand  or  the  left  hand,  or  witli 
the  hand  inverted  or  they  may  be  sent  back 
to  the  floor  several  limes  before  catching. 

Throwing  the  balls  against  the  wall,  tossing 
them  into  the  air,  and  many  other  exercises 


may  be  introduced  whenever  the  balls  are 
used,  and  will  always  serve  to  interest  the 
children.  Care  should  be  taken  to  have  every 
movement  performed  in  perfect  order,  and  that 
every  child  take  part  in  all  the  exercises  in  its 
turn. 

At  the  close  of  every  ball  play,  the  children 
occupy  their  original  places  marked  on  the 
floor,  the  balls  are  collected  by  one  or  two  of 
the  older  pupils,  and  after  this  has  been  done, 
each  child  takes  the  hand  of  its  opposite 
neighbor,  and  bowing,  says,  "  good  morning," 
when  they  march  by  twos,  accompanied  by 
music,  once  or  twice  through  the  hall,  and 
then  to  their  seats  for  other  occupation. 


THE    SECOND    GIFT. 


The  Second  Gift  consists  of  a  sphere,  a 
cube,  and  a  cylinder.  These  the  teacher  places 
upon  the  table,  together  with  a  rubber  ball, 
and  asks : 

"  Which  of  these  three  objects  looks  most 
like  the  ball?" 

The  children  will  certainly  point  out  the 
sphere,  but.  of  course,  without  giving  its  name. 

'Of  what  is  it  mad#?"  the  teacher  asks, 
placing  it  in  the  hand  of  some  pupil,  or  rolling 
it  across  the  table. 

The  answer  will  doubtless  be,  "  Of  wood." 
"  So  we  might  call  the  object  a  wooden  ball. 
But  we  will  give  it  another  name.  We  will 
call  it  a  sphere." 

Each  child  must  here  be  taught  to  pro- 
nounce the  word,  enunciating  each  sound  very 
distinctly.  The  ball  and  sphere  are  then  fur- 
ther compared  with  each  other,  as  to  material, 
color,  weight,  &c.,  to  find  their  similarities 
and  dissimilarities.  Both  are  round;  both 
roll  The  ball  is  soft;  the  sphere  is  hard. 
The  ball  is  light;  the  sphere  is  heavy.  The 
sphere  makes  a  louder  noise  when  it  falls  from 


the  table  than  the  ball.  The  ball  rebounds 
when  it  is  thrown  upon  the  floor ;  the  sphere 
does  not.  All  these  answers  are  drawn  out 
from  the  pupils  by  suitable  experiments  and 
questions,  and  every  one  is  required  to  repeat 
each  sentence  when  fully  explained. 

The  children  then  form  a  circle,  and  the 
teacher  rolls  the  sphere  to  one  of  them,  ask- 
ing the  child  to  stop  it  with  both  his  feet. 
This  child  then  takes  his  plac6  in  the  center, 
and  rolls  the  sphere  to  another  one,  who  again 
stops  it  with  his  feet,  and  so  on,  until  all  the 
children  have  in  turn  taken  their  place  in  the 
center  of  the  circle.  At  another  time,  the 
children  may  sit  in  two  rows  upon  the  floor, 
facing  each  other.  A  white  and  a  black 
sphere  ^re  then  given  to  the  heads  of  the 
rows,  who  exchange  by  rolling  them  across  to 
each  other.  Then  the  spheres  are  rolled 
across  obliquely  to  the  second  individuals  in 
the  rows.  These  exchange  as  before,  and 
then  roll  the  spheres  to  those  who  sit  third, 
and  so  on,  until  they  have  passed  throughout 
the  lines  and  back  again  to  the  head.     Both 


10 


GUIDE    TO    KINDER  GARTNERS. 


spheres  slx)uld  be  rolling  at  the  same  instant, 
which  can  be  effected  only  by  counting  or 
when  time  is  kept  to  accompanying  music. 

Another  variety  of  play  in  the  use  of  this 
gift  consists  in  placing  the  rubber  ball  at  a 
distance  on  the  floor,  and  letting  each  child, 
in  turn,  attempt  to  hit  it  with  the  sphere. 

For  the  purpose  of  further  instruction,  the 
sphere,  cube,  and  cylinder  are  again  placed 
upon  the  table,  and  the  children  are  asked 
to  discover  and  designate  the  points  of  re- 
semblance and  difference  in  the  first  two. 
They  will  find,  on  examination,  that  both  are 
made  of  wood,  and  of  the  same  color ;  but 
the  sphere  can  roll,  while  the  cube  cannot. 
Inquire  the  cause  for  this  difference,  and  the 
answer  will,  most  likely,  be  either,  "  the  sphere 
is  round,"  or  "  the  cube  has  corners." 

"  How  many  corners  has  the  cube  ? "  The 
children  count  them,  and  rtply,  "Eight" 

'•  If  I  put  my  finger  on  one  of  tnese  comers, 
and  let  it  glide  down  to  the  corner  below  it, 
(^thus,)  my  finger  has  passed  along  an  ed^e 
of  the  cube.  How  many  such  edges  can  we 
count  on  this  cube  .-•  I  will  let  my  finger 
glide  over  the  edges,  one  after  the  other,  and 
you  may  count." 

"One,  two,  three, 12." 

*'Our  cube,  then,  has  eight  corners,  and 
twelve  edges.  I  will  now  show  you  four  cor- 
ners and  four  edges,  and  say  that  this  part 
of  ihe  cube,  which  is  contained  between  these 
four  corners  and  four  edges,  is  called  a  side 
of  the  cube.  Count  how  many  sides  the  cube 
has." 

"  One  two,  three,  four,  five,  six.'" 

*'  Are  these  sides  all  alike,  or  is  one  small 
and  another  large  ?  "     "  They  are  all  alike." 

"  Then  we  may  say  that  our  cube  has  six 
sides,  all  alike,  and  that  each  side  has  four 
edges,  all  alike.  Each  of  these  sides  of  the 
cube  is  called  a  square." 

To  explain  the  cylinder,  a  conversation  like 
the  following  may  take  place.  It  will  be  ob- 
served that  instruction  is  here  given  mainly 
by  comparison,  which  is,  in  fact,  the  only 
philosophical  method. 


The  sphere,  cube,  and  cylinder  are  placed 
together  as  before,  in  the  presence  of  the 
children.  They  readily  recognize  and  name 
the  first  two,  but  are  in  doubt  about  the  third, 
whether  it  is  a  barrel  or  a  wheel.  They  mav 
be  suffered  to  indulge  their  fancy  for  av\hile 
in  finding  a  name  for  it,  but  are,  at  last  told 
that  it  is  2i*  cylinder,  and  are  taught  to  pro- 
nounce the  word  distinctly  and  accurately. 

"  What  do  you  see  on  the  cylinder  which 
you  also  see  on  the  cube  ? "  "  The  cylinder 
has  two-sides."  "  Are  the  sides  square,  like 
those  of  the  cube.?"     "  They  are  not." 

But  the  cylinder  can  stand  on  these  sides 
just  as  the  cube  can.  Let  us  see  if  it  cannot 
roll,  too,  as  the  sphere  does.  Yes  !  it  rolls ; 
but  not  like  the  sphere,  for  it  can  roll  only 
in  two  ways,  while  the  sphere  can  roll  any 
way.  So,  you  see,  the  sphere,  cube,  and 
cylinder  are  alike  in  some  respects,  and  differ- 
ent in  others.  Can  you  tell  me  in  what  re- 
spects they  are  just  alike.?" 

"  They  are  made  of  wood  ;  are  smooth  j 
are  of  the  same  color;  are  heavy;  make  a 
loud  noise  when  they  fall  on  the  floor." 

These  answers  must  be  drawn  out  by  ex- 
periments with  the  objects,  and  by  questions, 
logically  put,  so  as  to  lead  to  these  results  as 
natural  conclusibns.  I'he  exercise  may  be 
continued, "if  desirable,  by  asking  the  children 
to  name  objects  which  look  like  the  sphere, 
cube,  or  cylinder.  '1  ne  edge  of  a  cube  may 
also  be  explained  as  representing  a  straight 
line.  The  point  where  two  or  three  lines  or 
edges  meet  is  called  a  comer;  the  inner 
point  of  a  corner  is  an  angle,  of  which  each 
side,  or  square,  of  the  cube  has  four.  To 
sum  up  what  has  already  been  taught :  The 
cube  has  six  sides,  or  squares,  all  alike  ;  eight 
corners,  and  twelve  edges  ;  and  each  side  of 
the  cube  has  four  edges,  all  alike  ;  four  cor- 
ners, and  four  angles. 

The  sphere,  cube,  and  cylinder,  when  sus- 
pended by  a  double  thread,  can  be  made  to 
rotate  around  themselves,  for  the  purpose  of 
showing  that  the  sphere  appears  the  same  in 
form  in  whatever  manner  we  look  at  it ;  that 


GUIDE    TO    KINDER-GARTNERS. 


1 1 


the  cube,  when  rotating,  (suspended  at  the 
center  of  one  of  its  sides)  shows  the  form 
of  the  cylinder  ;  and  that  the  cylinder,  when 
rotating,  (suspended  at  the  center  of  its  round 
side,)  presents  the  appearance  of  a  sphere. 

Thus,  there  is,  as  it  were,  an  inner  triunity 
in  these  three  objects — sphere  contained  in 
cylinder,  and  cylinder  in  cube,  the  cylinder 
forming  the  mediation  between  the  two  others, 
or  the  transition  from  one  to  the  other.     Al- 


though the  child  may  not  be  told,  the  teacher 
may  think,  in  this  connection,  of  the  natural 
law,  according  to  which  the  fruit  is  contained 
in  the  flower,  the  flower  is  hidden  in  the  bud. 
Suspended  at  other  points,  cylinder  and 
cube  present  other  forms,  all  of  which  f?re 
interesting  for  the  children  to  look  at,  and  can 
be  made  instructive  to  their  young  minds,  if 
accompanied  by  apt  conversation  on  the  part 
of  the  teacher. 


THE    THIRD    GIFT. 


This  consists  of  a  cube,  divided  into  eight 
smaller  one-inch  cubes. 

A  prominent  desire  in  the  mind  of  every 
child  is  to  divide  things,  in  order  to  examine 
the  parts  of  which  they  consist.  This  natural 
instinct  is  observable  at  a  very  early  period. 
The  little  one  tries  to  change  its  toy  by  break- 
ing it,  desirous  of  looking  at  its  inside,  and  is 
sadly  disappointed  in  finding  itself  incapable 
of  reconstructing  the  fragments.  Froebel's 
Third  Gift  is  founded  on  this  observation. 
In  it  the  child  receives  a  whole,  whose  parts 
he  can  easily  separate,  and  put  together  again 
at  pleasure.  Thus  he  is  able  to  do  that  which 
he  could  not  in  the  case  of  the  toys — restore 
to  its  original  form  that  which  was  broken — 
making  a  perfect  whole.  And  not  only  this — 
he  can  use  the  parts  also  for  the  construction 
of  other  wholes. 

The  child's  first  plaything,  or  means  of 
occupation,  was  the  ball.  Next  came  the 
sphere,  similar  to,  yet  so  different  from,  the 
ball.  Then  followed  cube  and  cylinder,  both, 
in  some  points,  resembling  the  sphere,  }'et 
each  having  its  own  peculiarities,  which  dis- 
tinguish it  from  the  sphere  and  ball.  The 
pupil,  in  receiving  the  cube,  divisible  into 
eight  smaller  cubes,  meets  with  friends,  and  is 
delighted  at  the  multiplicity  of  the  gift     Each 


of  the  eight  parts  is  precisely  like  the  whole, 
except  in  point  of  size,  and  the  child  is  im- 
mediately struck  with  this  quality  of  his  fint 
toy  for  building  purposes.  By  simply  looking 
at  this  gift,  the  pupil  receives  the  ideas  of 
whole  and  part — oi  form  and  comparative  size ; 
and  by  dividing  the  cube,  is  impressed  with 
the  relation  of  one  part  to  another  in  regard 
to  position  and  order  of  movements,  thus 
learning  readily  to  comprehend  the  use  of 
such  terms  as  above,  belo^v,  before,  behind,  right, 
left,  &c.,  &c. 

With  this  and  all  the  following  gifts,  we 
produce  what  Froebel  c^W'i  forms  of  life,  forms 
of  knowledge,  and  forms  of  beauty. 

The  first  are  representations  of  objects  which 
actually  exist,  and  which  come  under  our  com- 
mon observation,  as  the  works  of  human  skill 
and  art.  The  second  are  such  as  afford  in- 
struction relative  to  number,  order,  proportion, 
&c.  The  third  are  figures  representing  only 
ideal  forms,  yet  so  regularly  constructed  as  to 
present  perfect  models  of  symmetry  and  order 
in  the  arrangement  of  the  parts.  Thus  in  the 
occupations  connected  with  the  use  of  these 
simple  building  blocks,  the  child  is  led  into 
the  living  world — there  first  to  take  notice  of 
objects  by  comparison ;  then  to  learn  some- 
thing of  their  properties  by  induction,   and 


12 


GUIDE  TO  KINDER-GARTNERS. 


lastly,  to  gather  into  his  soul  a  love  and  desire 
for  the  beautiful  by  the  contemplation  of  those 
forms  which  are  regular  and  symmetrical. 

THE  PRESENTATION  OF  THE  THIRD  GIFT. 

The  children  having  taken  their  usual  seats, 
the  teacher  addresses  them  as  follows: 

"  To-day,  we  have  something  new  to  play 
with." 

Opening  the  package  and  displaying  the 
box,  he  does  not  at  once  gratify  their  curiosity 
by  showing  them  what  it  contains,  but  com- 
mences by  asking  the  question — 

"  Which  one  of  the  three  objects  we  played 
with  yesterday  does  this  box  look  like  ?  " 

They  answer  readily,  "  The  cube." 

"  Describe  the  box  as  the  cube  has  been 
described,  with  regard  to  its  sides,  edges, 
corners,  &c." 

If  this  is  satisfactorily  done,  the  cover  may 
then  be  removed,  and  the  box  placed  inverted 
upon  the  table.  If  the  box  is  made  of  wood, 
it  is  placed  upon  its  cover,  which,  when  drawn 
out  will  allow  the  cubes  to  stand  on  the  table. 
Lifting  it  up  carefully,  so  that  the  contents 
may  remain  entire,  the  teacher  asks  : 

"  What  do  you  see  now  .''  " 

The  answer  is  as  before,  "  A  cube." 

One  of  the  scholars  is  told  to  push  it  across 
the  table.  I  n  so  doing,  the  parts  will  be  likely 
to  become  separated,  and  that  which  was  pre- 
viously wiiole  will  lie  before  them  in  frag- 
ments. The  children  are  iDermittcd  to  ex- 
amine the  small  cubes  ;  and  afier  each  one  of 
them  has  had  one  in  his  hand,  the  eight  cubes 
are  returned  to  the  teacher,  who  remarks  : 

"  Children. as  we  have  broken  the  thing,  we 
must  try  to  mend'xX..  Let  us  see  if  we  can  put 
It  together  as  it  was  before." 

This  having  been  done,  the  boxes  are  then 
distiibuted  among  the  children,  and  they  ate 
practiced  in  removing  the  covers,  and  t  iking 
out  the  cube  without  destroying  its  unity. 
They  will  find  it  difficult  at  first,  and  there 
will  be  many  failures.  But  let  them  continue 
to  try  until  some,  at  least,  have  succeeded, 
and  then  proceed  to  another  occupation. 


PREPARATION  FOR  CONSTRUCTING 
FORMS. 

The  surface  of  the  tables  is  covered  with  a 
net-work  of  ]ines,forming  squares  of  one  inch. 
'I'he  spaces  allotted  to  the  pupils  are  separated 
from  each  other  by  heavy  dark  lines,  and  the 
centers  are  marked  by  some  different  color. 
In  these  first  conversational  lessons,  the  chil- 
dren must  be  taught  to  point  out  the  right 
upper  corner  of  their  table  space,  the  left 
upper,  the  right  and  left  lower,  the  upper  and 
lower  edges,  the  right  and  left  edges,  a*id  the 
center.  With  little  staffs,  or  sticks  cut  at  con- 
venient lengths,  they  may  indicate  direction, 
e.  g.,  by  laying  them  upon  the  table  in  a  line 
from  left  to  right,  covering  the  center  of  the 
space,  or  extending  them  from  the  right  upper 
to  the  left  lower  corner  covering  the  center ; 
then  from  the  middle  of  the  upper  edge  to  the 
middle  of  the  lower  edge,  and  so  on.  The 
teacher  must  be  careftil  to  use  terms  that  can 
be  easily  comprehended,  and  avoid  changmg 
them  in  such  a  way  as  to  produce  any  am- 
biguity in  the  mind  of  the  child. 

Here,  as  in  the  more  advanced  exercises, 
everything  should  be  done  with  a  great  deal 
of  precision.  The  children  must  understand 
that  order  and  regularity  in  all  the  perform- 
ances are  of  the  utmost  importance.  The 
following  will  serve  as  an  illustration  of  the 
method  :  The  children  ha\"ing  received  the 
boxes, they  are  required  to  place  them  exactly 
in  the  center  of  their  spaces,  so  as  to  cover 
four  squares.  They  then  lake  hold  of  the  box 
with  the  left  hand,  and  remove  the  cover  with 
the  right,  placing  it  by  the  right  upper  corner 
of  the  net- work  on  the  table,  'i'hey  next 
place  the  left  hand  upon  the  open  box,  and 
reverse  it  with  the  right  hand,  so  that  the  left 
is  on  the  table.  Drawing  it  carefully  from 
beneath,  they  let  the  inveited  box  rest  on  the 
squares  in  the  center.  The  right  hand  is  used 
to  raise  the  box  carefully  from  its  place,  and, 
if  successful,  eight  small  cubes  will  stand  in 
tie  center  of  the  space,  forming  one  large 
cube.  Lastly,  the  box  is  placed  in  the  cover 
at  the  right  upper  corner,  and  qare  should 


GUIDE  TO  KINDER  GARTNERS. 


13 


be  taken  that  all  are  arranged  in  exact  posi- 
tion. 

(If  the  cubes  are  enclosed  in  wooden  boxes 
with  covers  to  be  drawn  out  at  the  side,  these 
manipulations  are  to  be  changed  accordingly.) 

At  the  close  of  any  play,  when  the  ma- 
terials are  to  be  returned  to  the  teacher,  the 
same  minuteness  of  detail  must  be  observed. 

Replacing  the  box  over  the  cubes,  placing 
the  left  hand  beneath,  and  lifting  the  box  with 
the  right,  reversing  it,  and  placing  it  again 
upon  the  center  of  the  table,  then  covering 
it — these  are  processes  which  must  be  re- 
peated many  times  before  the  scholar  can 
acquire  such  expertness  as  shall  render  it 
desirable  to  proceed  to  the  real  building  occu- 
pation. 

FORMS  OF  LIFE. 

The  boxes  being  opened  as  directed,  and 
the  cubes  upon  the  center  squares — in  each 
space — the  question  is  asked  : 

"  How  many  little  cubes  are  there  ? " 
"  Eight." 

"  Count  them,  placing  them  in  a  row  from 
left  to  right,"  (or  from  right  to  left.) 

"  What  is  that  ? "     "A  row  of  cubes." 

It  may  bear  any  appropriate  name  which 
the  children  give  it — as  "  a  train  of  cars,"  "  a 
company  of  soldiers,"  "  a  fence,"  &c. 

"  Now  count  your  cubes  once  more,  placing 
them  one  upon  another.  What  have  you 
there  ? " 

"  An  upright  row  of  eight  cubes." 

"  Have  you  ever  seen  anything  standing 
like  this  upright  row  of  cubes  ? " 

"  A  chimney,"     "  A  steeple." 

"  Take  down  your  cubes,  and  build  two 
upright  rows  of  them  —  one  square  apart. 
What  have  you  now  ?  " 

"Two  little  steeples,"  or  "  two' chimneys." 
Thus,  with  these  eight  cubes,  many  forms  of 
life  can  be  built  under  the  guidance  of  the 
teacher.  It  is  an  important  rule  in  this  occu- 
pation, that  nothing  should  be  rudely  destroyed 
which  has  been  constructed,  but  each  new  form 
is  to  be  produced  by  slight  change  of  the  pre- 
ceding one. 


On  Plates  I.  and  II.,  a  number  of  these  are 
given.  They  are  designated  by  Froebel  as 
follows  : 

1.  Cube,  or  Kitchen  Table. 

2.  Fire-Place. 

3.  Grandpa's  Chair. 

4.  Grandpa's  and  Grandma's  Chairs. 

5.  A  Castle,  with  two  towers. 

6.  A  Stronghold. 

7.  A  Wall. 

8.  A  High  Wall. 

9.  Two  Columns. 

ID.  A  Large  Column,  with  two  memorial 
stones. 

11.  Sign-Post. 

12.  Cross. 

13.  Two  Crosses. 

14.  Cross,  with  pedestal. 

15.  Monument. 

16.  Sentry-Box. 

17.  A  Well. 

18.  City  Gate. 

19.  Triumphal  Arch. 

20.  City  Gate,  with  Tower. 

21.  Church. 

22.  City  Hall. 

23.  Castle. 

24.  A  Locomotive. 

25.  A  Ruin. 

26.  Bridge,  with  Keeper's  House. 

27.  Two  Rows  of  Trees. 

28.  Two  Long  Logs  of  Wood, 

29.  A  Bole. 

30.  Two  Small  Logs  of  Wood. 

31.  Four  Garden  Benches. 

32.  Stairs. 

33.  Double  Ladder. 

34.  Two  Columns  on  Pedestals. 

35.  Well -Trough. 

36.  Bath. 

37.  A  Tunnel. 

38.  Easy  Chair. 

39.  Bench,  with  back. 

40.  Cube. 

Several  of  the  names  in  this  list  represenl 
objects  which,  being  more  specifically  German, 
will  not  be  recognized  by  the  children.     Ruins, 


14 


GUIDE    TO    KINDER  GARTNERS. 


castles,  sentry-boxes,  sign-posts,  perhaps  they 
have  never  Seen ;  but  it  is  easy  to  tell  them 
something  about  these  objects  which  will  in- ' 
terest  them.  They  will  listen  with  pleasure 
to  short  stories,  narrated  by  way  of  explana- 
tion, and  thus  associating  the  story  with  the 
form,  be  able,  at  another  time,  to  reconstruct 
the  latter  while  they  repeat  the  former  in  their 
own  words.  It  is  not  to  be  expected,  how- 
ever, that  teachers  in  this  country  should 
adhere  closely  to  the  list  of  Froebel.  They 
may,  with  advantage,  vary  the  forms,  and,  if 
they  choose,  affix  other  names  to  those  given 
upon  the  plates.  It  is  well  sometimes  to 
adopt  such  designations  as  are  suggested  by 
the  children  themselves.  They  will  be  found 
to  be  quite  apt  in  tracing  resemblances  be 
tween  their  structures  and  the  objects  with 
which  they  are  familiar. 

In  order  to  make  the  occupation  still  more 
useful,  they  should  be  required  also  to  point 
out  the  dissimilarities  existing  between  the 
form  and  that  which  it  represents. 

It  is  proper  to  allow  the  child,  at  times,  to 
invent  forms,  the  teacher  assisting  the  fantasy 
of  the  little  builder  in  the  work  of  construct- 
ing, and  in  assigning  names  to  the  structure. 
When  a  flgUre  has  been  found,  and  named, 
the  child  should  be  required  to  take  the  blocks 
apart,  and  build  the  same  several  times  in  suc- 
cession. Older  and  more  advanced  scholars 
suggest  to  younger  and  less  abler  ones,  and 
the  latter  will  be  found  to  appreciate  such 
help. 

It  is  a  common  observation,  that  the  younger 
children  in  a  family  develop  more  rapidly  than 
the  older  ones,  since  the  former-  are  assisted 
in  their  mental  growth  by  companionship  wdth 
the  latter.  This  benefit  of  association  is  seen 
more  fully  in  the  Kinder  Garten,  under  the 
judicious  guidance  of  a  tencher  who  krows 
now  to  encourage  what  is  right,  and  check 
what  is  wrong,  in  the  disposition  of  the  chil- 
dren. 

It  should  be  remarked,  in  connection  with 
these  directions,  that  in  the  use  of  this  and 
the  succeeding  gift  it  is  essential  that  all  the 


blocks  should  be  used  in  the  building  of  each 
figure,  in  order  to  accustom  the  child  to  look 
upon  things  as  mutually  related.  There  is 
nothing  which  has  not  its  appointed  place, 
and  each  part  is  needed  to  constitute  the 
whole.  For  example,  the  well-trough  (35) 
may  be  built  of  six  cubes,  but  the  remaining 
two  should  represent  two  pails  with  which  the 
water  is  conveyed  to  the  trough. 

FORMS  OF  KNOWLEDGE. 

These  do  not  represent  objects,  either  real 
or  ideal.  They  instruct  the  pupil  concerning 
the  properties  and  relations  of  numbers,  by 
a  particular  arranging  and  grouping  of  the 
blocks.  Strictly  speaking,  the  first  effort  to 
count,  by  laying  them  on  the  table  one  after 
another,  is  to  be  classed  under  this  head. 
The  form  thus  produced,  though  varied  at 
each  trial,  is  one  of  tlie  forms  of  knowledge, 
and  by  it  the  child  receives  its  first  lesson  in 
arithmetic. 

Proceeding  further,  he  is  taught  to  add, 
always  by  using  the  cubes  to  illustrate  the 
successive  steps.  Thus,  having  placed  two 
of  the  blocks  at  a  little  distatice  from  each 
other  on  the  table,  he  is  caused  to  repeat, 
"  One  and  one  are  two."  Then  placing 
another  upon  the  table,  he  repeats,  "  One 
and  two  are  three,"  and  so  on,  until  all  the 
blocks  are  added. 

Subtraction  is  taught  in  a  similar  manner, 
Having  placed  all  the  cubes  upon  the  table, 
the  scholar  commences  taking  them  off,  one 
at  a  time,  repeating,  as  he  does  this,  "  One 
from  eight  leaves  seven ;  "  One  from  seven 
i-nvcs  six,"  and  so  on. 

According  to  circumstances,  of  which  the 
Kinder-Gartner,  of  course,  will  be  the  best 
judge,  these  exercises  may  be  continued  fur- 
ther, by  adding  and  subtracting  two,  three, 
and  so  on ;  but  care  should  always  be  taken 
that  no  new  step  be  made  until  all  that  has 
gone  before  is  perfectly  understood. 

With  the  more  advanced  classes,  exercises 
in  multiplication  and  division  may  be  tried, 
by  grouping'  the  blocks 


GUIDE    TO    KINDER  GARTNERS. 


i5 


The  division  of  the  large  cube,  to  illustrate 
the  principles  of  proportion,  is  an  interesting 
and  iHStruciive  occupation ;  and  we  will  here 
proceed  to  give  the  method  in  detail. 

The  children  have  their  cube  of  eight  be- 
fore them  on  the  table.  The  teacher  is  also 
furnished  with  one.  and  lifting  the  upper  half 
in  the  manner  shown  on  Plate  I.,  No.  4, 
asks : 

"  Did  I  take  the  whole  of  my  cube  in  my 
hand,  or  did  I  leave  some  of  it  on  the  table  ? " 

'•You  left  some  on  the  table." 

"  Do  I  hold  •  in  my  hand  more  of  my  cube 
than  I  left  on  the  table,  or  are  both  parts 
alike?" 

"  Both  are  alike." 

"  If  things  are  alike,  we  call  them  equal. 
So  I  divided  my  cube  into  two  equal  parts, 
and  each  of  these  equal  parts  I  call  a  half. 
Where  are  the  two  halves  of  my  cube  ? " 

"  One  is  in  your  hand ;  the  other  is  on  the 
table." 

"  So  I  have  two  half  cubes.  I  will  now 
place  the  half  which  I  have  in  my  hand  upon 
the  half  standing  on  the  table.  What  have  I 
now  ? " 

"  A  whole  cube." 

The  teacher,  then  separating  the  cube  again 
into  halves,  by  drawing  four  of  the  smaller 
cubes  to  the  right  and  four  to  the  left,  as  is 
indicated  on  Plate    L,    No.  2,  asks  : 

"  What  have  I  now  before  me  ? " 

"  Two  half  cubes." 

"  Before,  I  had  an  upper  and  a  lower  half. 
Now,  I  have  a  right  and  a  left  half.  Uniting 
the  halves  again  I  have  once  more  a  whole." 

The  scholars  are  taught  to  repeat  as  fol- 
lows, while  the  teacher  divides  and  unites  the 
cubes  in  both  ways,  and  also  as  represented 
by  Form  No.  3: 

"  One  whole — two  halves," 

"  Two  halves — one  whole." 

Again,  each  half  is  divided,  as  shown  in 
Forms  No.  5,  6,  and  7,  and  the  children  are 
required  to  repeat  during  these  occupations: 

"  One  whole — two  halves." 

"  One  half — two  quarters  (or  fourths)." 


'•  Two  quarters — one  half." 

"Two  halves — one  whole," 

After  these  processes  are  fully  explained 
and  the  principles  well  understood  by  the 
scholars,  they  are  to  try  their  hand  at  divid- 
ing of  the  cube — first,  individually  then  all 
together.  If  they  succeed,  they  may  then  be 
taught  to  separate  it  into  eighths.  It  is  not 
advisable,  in  all  cases,  to  proceed  thus  far. 

Children  under  four  years  of  age  should  be 
restricted,  for  the  most  part,  to  the  use  of  the 
cubes  for  practical  building  purposes,  and  for 
simpler  forms  of  knowledge. 

FORMS  OF  BEAUTY. 

Starting  with  a  few  simple  arrangements, 
or  positions,  of  the  blocks,  we  are  able  to 
develop  the  forms  contained  in  this  class  by 
means  of  a  fixed  law,  viz.,  that  every  change 
of  position  is  to  be  accompanied  by  a  cor- 
responding movement  on  the  opposite  side. 
In  this  way  symmetrical  figures  are  construct- 
ed in  infinite  variety,  representing  no  real 
objects,  5'et,  by  their  regularity  of  outline, 
adapted  to  please  the  eye,  and  minister  to  a 
correct  artistic  taste.  The  love  of  the  beau- 
tiful cannot  fail  to  be  awakened  in  the  youth- 
ful mind  by  such  an  occupation  as  this,  and 
with  this  emotion  will  be  associated,  to  some 
extent,  the  love  of  the  good,  for  they  are  in- 
separable. 

The  works  of  God  are  characterized  by 
perfect  order  and  symmetry,  and  his  good- 
ness is  commensurate  with  the  beauty  mani- 
fest everywhere  in  the  fruits  of  his  creative 
power.  The  construction  of  forms  of  beauty 
with  the  building  blocks  will  prepare  the  child 
to  appreciate,  by  and  by,  the  order  that  rules 
the  universe. 

By  Plates  IV.  and  V.  it  will  be  seen  that 
these  forms  are  of  only  one  block's  height, 
and.  consequently,  represent  outlines  of  sur- 
faces. It  is  necessary  that  the  children  should 
be  guided,  in  their  construction,  by  an  easily 
recognizable  center.  Around  this  visible  point 
all  the  separate  parts  of  the  form  to  be  created 
must  be  arranged,  just  as  in  working  out  th*^ 


l6 


GUIDE    TO    KINDER-GARTNERS. 


highest  destiny  of  man,  all  his  thoughts  and 
acts  need  to  be  regulated  by  an  invisible  cen- 
ter, around  which  he  is  to  construct  a  har- 
monious and  beautiful  whole. 

In  order  to  produce  the  varied  forms  of 
beauty  with  the  simple  material  placed  in  the 
hands  of  the  scholar,  he  must  first  learn  in 
what  ways  two  cubes  may  be  brought  in  con- 
tact with  each  other.  Four  positions  are 
shown  on  Plate  IV.  The  blocks  may  be  ar- 
ranged either — side  by  side,  as  in  Fig.  i  ;  edge 
to  edge,  as  in  Fig.  2  ;  or  edge  to  side,  and  side 
to  edge,  as  in  Nos.  3  and  4.  Nos  i  and  3  are 
the  cpposites  to  2  and  4.  Other  changes  of 
position  may  be  made.  For  example,  in  Fig.  1 
the  block  marked  a  may  be  placed  above  or  to 
the  right  or  to  the  left  of  the  block  marked  b. 
The  cubes  may  also  be  placed  in  certain  rela- 
tions to  each  other  on  the  table,  without  being 
in  actual  contact.  These  positions  should  be 
practiced  perseveringly  at  the  outset,  so  as  to 
furnish  a  foundation  for  the  processes  of  con- 
struction which  are  to  follow.  It  is  one  of  the 
important  features  of  Froebel's  system,  that  it 
enables  the  child  readily  to  discover,  and 
critically  to  observe,  all  relations  which  ob- 
jects sustain  to  one  another.  Thoroughness, 
therefore,  is  required  in  all  the  details  of  these 
occupations. 

We  start  from  any  fundamental  form  that 
may  present  itself  to  our  mind.  Take,  for 
illustration,  Form  No.  5.  Four  cubes  are 
here  united  side  to  side,  constituting  a  square 
surface,  and  the  outline  is  completed  by  plac- 
ing" the  four  remaining  cubes  severally  side  to 
side  with  this  middle  square.  In  6,  edge 
touches  edge ;  in  7,  side  touches  edge,  and  in 


8,  edge  touches  side  midway.     Another  mode 
of  development  is  shown  in  Forms  9 — 15. 

The  four  outside  cubes  move  toward  the 
right  by  a  half  cube's  length,  until  the  original 
form  reappears  in  No.  15. 

Now,  the  four  outside  cubes  occupy  the 
opposite  position.  Fig.  16,  edges  touch  sides. 
'Ihey  are  moved  as  before,  by  a  half  cube's 
length,  until,  in  Form  No.  22,  the  one  with 
which  we  started,  is  regained. 

We  now  extract  the  inside  cubes  (^),  Fig. 
23,  and  each  of  them  travels  around  its  neigh- 
bor cube  (rt),  until  a  standing,  hollow  square 
is  developed,  as  in  Fig,  29. 

Now  cube  a  again  is  set  in  motion.  It 
assumes  a  slanting  direction  to  the  remain- 
ing cubes.  Fig.  30,  and,  pursuing  its  course 
around  them,  the  Form,  No.  29,  reappears 
in  No.  36. 

Next,  b  is  drawn  out,  Fig.  37.  and  d  pushed 
in,  until  a  standing  cross  is  formed,  Fig.  38. 
b,  constantly  traveling  on  by  a  half  cube's 
length,  until.  Fig.  43  all  cubes  are  united  in  a 
large  square,  and  b  again  begins  traveling,  by 
a  cube's  length,  turning  side  to  side  and  edge 
to  edge.  In  Fig.  48,  b  performs  as  a  has 
done. 

But  with  more  developed  children  we  may 
proceed  on  other  principles,  Fig.  49,  intro 
ducing  changes  only  on  two  instead  of  four 
sides,  and  thus  arriving  successively  at  Forms 
50—60. 

After  each  occupation,  the  scholars  should 
replace  their  cubes  in  the  boxes,  as  heretofore 
described,  and  the  material  should  be  re- 
turned to  the  closet  where  it  is  kept  before 
commencing  any  other  play. 


K>^ 


J<^ 


THE    FOURTH    GIFT. 


The  preceding  gift  consisted  of  cubical 
blocks,  all  of  their  three  dimensions  being  the 
same.  In  the  Fourth  Gift,  we  have  greater 
variety  for  purposes  of  construction,  since  each 
of  the  parts  of  the  large  cube  is  an  oblong, 
whose  length  is  twice  its  width,  and  four  times 
its  thickness.  The  dimensions  bear  the  same 
proportion  to  each  other  as  those  of  an  or- 
dinary brick ;  and  hence  these  blocks  are 
sometimes  called  bricks.  They  are  useful  in 
teaching  the  child  difference  in  regard  to 
length,  breadth,  and  height.  This  difference 
enables  them  to  construct  a  greater  variety 
of  forms  than  he  could  by  means  of  the  third 
gift.  By  these  he  is  made  to  understand, 
more  distinptl)',  the  meaning  of  the  terms  per- 
pendicular and  horizontal.  And  if  the  teacher 
sees  fit  to  pursue  the  course  of  experiment 
sufficiently  far,  many  philosophical  truths  will 
be  developed ;  as,  for  instance,  the  law  of 
equilibrium,  shown  by  laying  one  block  across 
another,  or  the  phenomenon  of  continuous 
motion,  exhibited  in  the  movement  of  a  row 
of  the  blocks,  set  on  end,  and  gently  pushed 
from  one  direction. 

PREPARATION    FOR   CONSTRUCTING 
FORMS. 

This  gift  is  introduced  to  the  children  in  a 
manner  similar  to  the  presentation  of  the  third 
gift.  The  cover  is  removed,  and  the  box  is 
reversed  upon  the  table.  Lifting  the  box 
carefully,  the  cube  remains  entire.  The  chil- 
dren are  made  to  observe  that,  when  whole, 
its  size  is  the  same  as  that  of  the  previous  one. 
Its  parts,  however,  are  very  different  in  form, 
though  their  number  is  the  same.  There  are 
still  eight  blocks.  Let  the  scholars  compare 
one  of  the  small  cubes  of  the  third  gift  with 
one  of  the  oblongs  in  this  gift ;  note  the  simi- 
3 


larities  and  the  differences ;  then,  if  they  can 
comprehend  that  notwithstanding  they  are  so 
unlike  in  form,  their  solid  contents  is  the  same, 
since  it  takes  just  eight  of  each  to  make  the 
same  sized  cube,  an  important  lesson  will 
have  been  learned.  If  told  to  name  objects 
that  resemble  the  oblong,  they  will  readily 
designate  a  brick,  table,  piano,  closet,  &c.,  and 
if  allowed  to  invent  forms  of  life,  will,  doubt- 
less, construct  boxes,  benches,  &c. 

The  same  precision  should  be  observed  in 
all  the  details  of  opening  and  closing  the 
plays  with  this  gift  as  in  those  previously  de- 
scribed. 

FORMS  OF  LIFE. 


The  following  is  a  list  of  Froebel's  forms. 

which 

are  represented  on  Plates  VI 

.  and  VII. 

If  the 

;  names  do  not  appear  quite  s 

triking,  or 

to  the 

point,  the  teacher  may  try  to  substitute 

better 

ones : 

1. 

The  Cube. 

2. 

Part  of  a  Floor,  or  Top  of  a 

Table. 

3- 

Two  Large  Boards. 

4- 

Four  Small  Boards. 

5- 

Eight  Building  Blocks. 

6. 

A  Long  Garden  Wall. 

7- 

A  City  Gate. 

8. 

Another  City  Gate. 

9- 

A  Bee  Stand. 

ID. 

A  Colonnade. 

II. 

A  Passage. 

12. 

Bell  Tower. 

13- 

Open  Garden  House. 

14. 

Garden  House,  with  Doors. 

IS- 

Shaft. 

16. 

Shaft. 

17 

A  Well,  with  Cover. 

18. 

Fountain. 

19. 

Closed  Garden  Wall 

i8 


GUIDE    TO    KINDER-GARTNERS. 


20.  An  Open  Garden. 

21.  An  Open  Garden.    • 

22.  Watering-Trough. 

23.  Shooting-Stand. 

24.  Village. 

25.  Triumphal  Arch. 

26.  Caroussel. 

27.  Writing  Desk. 

28.  Double  Settee. 

29.  Sofa. 

30.  Large  Garden  Settee. 

31.  Two  Chairs. 

32.  Garden  Table  Chairs 

33.  Children's  Table. 

34.  Tombstone. 

35.  Tombstone. 

36.  Tombstone. 

37.  Monument. 

38.  Monument. 

39.  Winding  Stairs. 

40.  Broader  Stairs. 

41.  Stalls. 

42.  A  Cross  Road. 

43.  Tunnel. 

44.  Pyramid. 

45.  Shooting-Stand. 

46.  Front  of  a  House. 

47.  Chair,  with  Footstool. 

48.  A  Throne. 

49.  J  Illustration  of 

50.  \  Continuous  Motion. 

Here,  as  in  the  use  of  the  previous  gift, 
one  form  is  produced  from  another  by  slight 
changes,  accompanied  by  explanations  on  the 
part  of  the  teacher.  Thus,  Form  30  is  easily 
changed  to  31,  32,  and  ^;^.  and  Form  34  may 
be  changed  to  35.  36,  and  37.  In  every  case, 
all  the  blocks  are  to  be  employed  in  con- 
structing a  figure. 

FORMS  OF  KNOWLEDGE. 

This  gift,  like  the  preceding,  is  used  to 
communicate  ideas  of  divisibility.  Here,  how- 
ever, on  account  of  the  particular  form  of 
the  parts,  the  processes  are  adapted  rather  to 
illustrate  the  division  of  a  surface,  than  of  a 
solid  body. 


The  cube  is  first  arranged  so  that  one  per- 
pendicular and  three  horizontal  cuts  appear, 
and  a  child  is  then  requested  to  separate  it  into 
halves,  these  halves  into  quarters,  and  these 
quarters  into  eighths  Each  of  the  latter  will 
be  found  to  be  one  of  the  oblong  blocks,  and 
this  for  the  time,  may  be  made  the  subject  of 
conversation. 

"  Of  what  material  is  this  block  made  ? " 

"What  is  the  color?" 

''What  objects  resemble  it  in  form?" 

"How  many  sides  has  it?" 

"  Which  is  the  largest  side  ? " 

''Which  is  the  smallest  side?" 

"  Is  there  a  side  larger  than  the  smallest 
and  smaller  than  the  largest?" 

In  this  way,  the  scholars  learn  that  there 
are  three  kinds  of  sides,  symmetrically  arrang- 
ed in  pairs.  The  upper  and  lower,  the  right 
and  left,  the  front  and  back,  are  respectively 
equal  to  and  like  each  other. 

By  questions,  or  by  direct  explanation,  facts 
like  the  following,  may  be  made  apparent  to 
the  minds  of  children.  "  The  upper  and  low- 
er sides  of  the  block  are  twice  as  large  as  the 
two  long  sides,  or  the  front  and  back,  as  they 
may  be  called.  Again,  the  front  and  back  are 
twice  as  large  as  the  right  and  left,  or  the  two 
short  sides  of  the  block.  Consequently,  the 
two  largest  sides  are  four  times  as  large  as 
the  two  smallest  sides."  This  can  be  demon- 
strated in  a  very  interesting  way,  by  placing 
several  of  the  blocks  side  by  side,  in  a  varie- 
ty of  positions,  and  in  all  these  operations 
the  children  should  be  allowed  to  experiment 
for  themselves.  The  small  cubes  of  the  pre- 
ceding gift  may  also  with  propriety  be  brought 
in  comparison  with  the  oblongs  of  this  gift,  and 
the  differences  observed. 

When  the  single  block  has  been  employed 
to  advantage,  through  several  lessons,  the 
whole  cube  may  then  be  made  use  of,  for  the 
representation  of  forms  of  knowledge. 

Construct  a  tablet  or  plane  as  in  Plate  VIII. 
a.  In  order  to  show  the  relations  of  dimen- 
sion, divide  this  plane  into  halves,  either  by  a 
perpendicular  or  horizontal  cut  (b  and-  c). 


GUIDE    TO    KINDER-GARTNERS. 


19 


These  two  forms  will  give  rise  to  instruct- 
ive observations  and  remarks  by  asking : 

"  What  was  the  form  of  the  original  tablet?" 

"  What  is  the  form  of  its  halves  ?  " 

"  How  many  times  larger  is  their  breadth 
than  their  height  ? " 

So  with  regard  to  the  position  of  the  oblong 
halves  ;  the  one  at  b  may  be  said  to  be  lying 
while  that  at  c  is  standing. 

"  Change  a  lying  to  a  standing  oblong."  In 
order  to  do  this,  the  child  will  move  the  first 
so  as  to  describe  a  quarter  of  a  circle  to  the 
right  or  left. 

"  Unite  two  oblongs  by  joining  their  small 
sides.   You  then  have  a  large  lying  oblong "(<?), 

"Separate  again  {/)  and  divide  each  part 
into  halves,  (/).  You  have  now  four  parts 
called  quarters,  and  these  are  squares,  in  their 
surface  form." 

Each  of  these  quarters  may  be  subdivided, 
and  the  children  taught  the  method  of  division 
by  two.  Other  material  may  also  be  used  in 
connection  with  the  blocks,  such  as  apples,  or 
any  small  objects  which  serve  to  illustrate  the 
properties  of  number.  It  is  evident  that  these 
operations  should  be  conducted  in  the  most 
natural  way,  and  never  begun  at  too  early  a 
stage  of  development  of  the  little  ones.  In 
figures  <r,  g.  h  and  k  on  Plate  VIII.  another 
mode  is  indicated,  for  the  purpose  of  illus- 
trating further  the  conditions  of  form  connect- 
ed with  this  gift.  Figs.  1 — 16  Plate  VIII. 
show  the  manner  in  which  exercises  in  addition 
and  subtraction  may  be  introduced,  as  has  al- 
ready been  alluded  to  in  the  description  of  the 
Third  Gift. 

FORMS  OF  BEAUTY. 

We  first  ascertain,  as  in  the  case  of  the 
cubes,  the  various  modes  in  which  the  oblongs 
can  be  brought  in  relation  to  each  other. 
These  are  much  more  numerous  than  in  the 
Third  Gift,  because  of  the  greater  variety  in 


the  dimensions  of  the  parts.  Plate  IX.  shows 
a  number  of  forms  of  beauty  derivable  from 
the  original  form,  I.  Each  two  blocks  form 
a  separate  group,  which  four  groups  touching 
in  the  center,  form  a  large  square.  The  out- 
side blocks  {a)  move  in  Figs,  i — 9,  around  the 
stationary  middle. 

The  inside  blocks  {p)  are  now  drawn  out 
(Fig.  10),  then  the  blocks  {a)  united  to  form 
a  hollow  square  (Fig.  11),  around  which  b 
moves  gradually  (Figs.  12  and  13). 

Now  b  is  combined  into  a  cross  with  open 
center,  a  goes  out  (Fig  14)  and  moves  in  an 
opposite  direction  until  Fig.  17  appears. 

By  extricating  b  the  eight-rayed  star  (Fig 
18)  is  formed.  In  Fig.  19  a  revolves,  b  is 
drawn  out  until  edge  touches  edge,  and  thus 
the  form  of  a  flower  appears  (Fig.  20). 

Now  b  is  turned  (Fig.  21),  and  in  Fig.  22, 
a  wreath  is  shown.  In  Fig.  22,  the  in.side 
edges  touch  each  other;  in  Fig.  23,  inside 
and  outside  ;  in  Fig.  24,  edges  with  sides,  and 
b  is  united  to  a  large  hollow  square,  around 
which  a  commences  a  regular  moving.  In 
Fig.  29,  a  is  finally  united  to  a  lying  cross,  and 
thereby  another  starting-point  gained  for  a 
new  series  of  developments. 

Each  of  these  figures  can  be  subjected  to 
a  variety  of  changes  by'  simply  placing  the 
blocks  on  their  long  or  short  sides,  or  as  the 
children  will  say,  by  letting  them  stand  up  or 
lie  down.  The  net-work  of  lines  on  the 
table  is  to  be  the  constant  guide,  in  the  con- 
struction of  forms.  In  inventing  a  new  series, 
place  a  block  above,  below,  at  the  right  or 
left  of  the  center  ;  and  a  second  opposite  and 
equidistant,  A  third  and  a  fourth  are  placed 
at  the  right  and  left  of  these,  but  in  the  same 
position  relative  to  the  center.  The  remain- 
ing four  are  placed  symmetrically  about  those 
first  laid.  By  moving  the  ^'s  or  ^'s  regularly 
in  either  direction,  a  variety  of  figures  ma) 
be  formed. 


THE    FIFTH    GIFT. 

CUBE,  TWICE   DIVIDED   IN   EACH   DIRECTION. 

(plates    X.   TO    XVI.) 


All  gifts  used  as  occupation  material  in  the 
Kinder-Garten  develop,  as  previously  stated, 
one  from  another.  The  Fifth  Gift,  like  that 
of  the  Third  and  Fourth  Gifts,  consists  of  a 
cube  again,  although  larger  than  the  previous 
ones.  The  cube  of  the  Third  Gift  was  divided 
once  in  all  directions.  The  natural  progress 
from  I  is  to  2  ;  hence  the  cube  of  the  Fifth 
Gift  is  divided  twice  in  all  directions  ;  conse- 
quently, in  three  equal  parts,  each  consisting 
of  nine  smaller  cubes  of  equal  size.  But  as 
this  division  would  only  have  multiplied,  not 
diversified,  the  occupation  material,  it  was 
necessary  to  introduce  a  new  element,  by 
subdividing  some  of  the  cubes  in  a  slanting 
di  "ection. 

We  have  heretofore  introduced  only  perpen- 
dicular and  horizontal  lines.  These  opposites, 
however,  require  their  mediate  element,  and 
this  mediation  was  already  indicated  in  the 
forms  of  life  and  of  beauty  of  the  Third  and 
Fourth  Gifts,  when  side  and  edge,  or  edge 
and  side,  were  brought  to  touch  each  other. 
The  slanting  direction  appearing  there  trans- 
itionally — occasionally — here,  becomes  per- 
manent by  introducing  the  slanting  line,  sepa 
rated  by  the  division  of  the  body,  as  a  bodily 
reality. 

Three  of  the  part  cubes  of  the  Fifth  Gift 
are  divided  into  half  cubes,  three  others  into 
quarter  cubes,  so  that  there  are  left  twenty- 
one  whole  cubes  of  the  twenty-seven,  produced 
by  the  division  of  the  cube  mentioned  before, 
and  the  whole  Gift  consists  of  thirty-nine  sin- 
gle pieces. 

•^      4 


It  is  most  convenient  to  pack  Ihem  in  the 
box,  so  as  to  have  all  half  and  quarter  cubes 
and  three  whole  cubes  in  the  bottom  row,  (see 
Plate  XV.,  i°.)  which  only  admits  of  separating 
the  whole  cube  in  the  various  ways  required 
hereafter,  as  it  will  also  assist  in  placing  the 
cube  upon  the  table,  which  is  done  in  the 
same  manner  as  described  with  the  previous 
Gifts. 

The  first  practice  with  this  Gift  is  like  that 
with  others  introduced  thus  far.  Led  by  the 
question  of  the  teacher,  the  pupils  state  that 
this  cube  is  larger  than  their  other  cubes; 
and  the  manner  in  which  it  is  divided  will 
next  attract  their  attention.  They  state  how 
many  times  the  cube  is  divided  in  each  direc- 
tion, how  many  parts  we  have  if  we  separate 
it  according  to  these  various  divisions,  and 
carrying  out  what  we  say,  gives  them  the 
necessary  assistance  for  answering  these  ques- 
tions correctly.  In  No.  3,  Plate  XV.,  the  three 
parts  of  the  cube  have  been  laid  side  by  side 
of  each  other. 

These  three  squares  we  can  again  divide 
in  three  parts,  and  these  latter  again  in  three, 
so  that  then  we  shall  have  twenty-seven  parts, 
which  teaches  the  pupil  that  3X3^9-3X9 
=  27. 

To  some,  the  repetition  of  the  apparently 
simple  exercises  may  appear  superfluous  ;  but 
repetition  alone,  in  this  simple  manner,  will 
assist  children  to  remember,  and  it  is  always 
interesting,  as  they  have  not  to  deal  with  ab- 
stractions, but  have  real  tilings  to  look  at  foi 
the  formation  of  their  conclusions. 


22 


GUIDE   TO    KINDER-GARTNERS. 


But,  again  I  say,  do  not  continue  these 
occupations  any  longer  than  you  can  com- 
mand the  attention  of  your  pupils  by  them. 
As  soon  as  signs  of  fatigue  or  lack  of  interest 
become  manifest,  drop  the  subject  at  once, 
and  leave  the  Gift  to  the  pupils  for  their  own 
amusement.  If  you  act  according  to  this  ad- 
vice, your  pupils  never  will  over-exert  them- 
selves, and  will  always  come  with  enlivened 
interest  to  the  same  occupation  whenever  it 
is  again  taken  up. 

After  the  children  have  become  acquainted 
with  the  manner  of  division  of  their  new 
large  cube,  and  have  exercised  with  it  in  the 
above-mentioned  way,  their  attention  is  drawn 
to  the  shape  of  the  divided  half  and  quarter 
cubes. 

They  are  divided  by  means  of  slanting  lines, 
which  should  be  made  particularly  prominent, 
and  the  pupils  are  then  asked  to  point  out, 
on  the  whole  cubes,  in  what  manner  they 
were  divided  in  order  to  form  half  and  quar- 
ter cubes.  The  pupils  also  point  out  hori- 
zontal, perpendicular  and  slanting  lines  which 
they  observe  in  things  in  the  room  or  other 
near  objects. 

Take  the  two  halves  of  your  cube  apart, 
and  say,  "  How  many  corners  and  angles  you 
can  count  on  the  upper  and  lower  sides  of 
these  two  half  cubes  ?  "  "  Three."  Three 
corners  and  three  angles,  which  latter,  you 
recollect,  are  the  insides  of  corners.  We  call, 
therefore,  the  upper  and  lower  side  of  the 
half  cube  a  triangle,  which  simply  means  a 
side  or  plane  with  three  angles.  The  child 
has  now  enriched  its  knowledge  of  lines  by 
the  introduction  of  the  oblique  or  slanting 
line,  in  addition  to  the  horizontal  and  perpen- 
dicular lines,  and  of  sides  or  planes  by  the 
introduction  of  the  triangle,  in  addition  to 
the  square  and  oblong  previously  introduced. 
With  the  introduction  of  the  triangle,  a  great 
treasure  for  the  development  of  forms  is 
added,  on  account  of  its  frequent  occurrence 
as  elementary  forms  in  all  the  many  forma- 
tions of  regular  objects. 

The  child  is  expected  to  know  this  Gift  now 


sufficiently  to  employ  it  for  the  production 
of  the  various  forms  of  life  and  beauty  now 
to  be  introduced. 

FORMS   OF   LIFE. 

(plates    X.    AND     XI.) 

The  main  condition  here,  as  always,  is 
that  for  each  representation  the  whole  of 
the  occupation  material  be  employed ;  not 
that  only  one  object  should  always  be  built, 
but  in  such  manner  that  remaining  pieces 
be  always  used  to  represent  accessory  parts, 
although  apart  from,  yet  in  a  certain  rela- 
tion to  the  main  figure.  The  child  should, 
again  and  again,  be  reminded  that  nothing 
belonging  to  a  whole  is,  or  could  be,  allowed 
to  be  superfluous,  but  that  each  individual 
part  is  destined  to  fill  its  position  actively 
and  effectively  in  its  relation  to  some  greater 
whole. 

Nor  should  it  be  forgotten  that  nothing 
should  be  destroyed,  but  everything  produced 
by  re-building.  It  is  advisable  always  to  start 
with  the  figure  of  the  cube. 

There  are  only  the  few  following  models  on 
our  Plates  lo  and  ii  : 

1.  Cube. 

2.  Flower-stand. 

3.  Large  Chair. 

4.  Easy  Chair,  with  Foot  Bench. 

5.  A  Bed.  Lowest  row,  fifteen  whole  cubes ; 
second  row,  six  whole  and  six  half  cubes,  com- 
posed of  twelve  quarter  cubes ;  third  row,  six 
half  cubes. 

6.  Sofa.  First  row,  sixteen  whole  and  two 
half  cubes  ;  6%  ground   plan 

7.  A  Well.     7%  ground  plan. 

8.  House,  with  Yard.  8",  ground  plan; 
twelve  whole  cubes,  ground ;  nine  whole  and 
six  half  cubes,  second  row  ;  roof,  twelve  quar- 
ter cubes. 

9.  A  Peasant's  House.  First  row,  ten 
whole  cubes  ;  second  row,  eight  whole  and 
two  half  cubes;  roof,  eight  cubes,  three 
halves  and  two  halves,  and  eight  quarters 
and  two  halves  and  four  quarters ;  9",  ground 
plan. 


GUIDE    TO    KINDER-GARTNERS. 


23 


10.  School-House.  Third  row,  three  whole 
and  six  half  cubes  ;  fourth  row,  one  whole 
and  four  quarter  cubes  ;  10",  ground  plan. 

11.  Church.  Building  itself. eighteen  whole 
cubes ;  roof,  twelve  quarter  cubes ;  steeple, 
four  whole  cubes  and  one  half  cube  ;  vestry, 
one  whole  and  one  half  cube  ;  1 1*,  ground 
plan  of  Church. 

12.  Church,  with  Two  Steeples.  Building 
itself,  twelve  whole  cubes ;  roof,  twelve  quar- 
ter cubes ;  steeples,  twice  five  whole  cubes 
and  one  half  cube ;  between  steeples,  one 
whole  cube  ;  12',  ground  plan. 

13.  Factory,  with  Chimney  and  Boiler- 
house.  Factory,  sixteen  whole  cubes ;  roof, 
six  half  and  four  quarter  cubes  ;  chimney,  five 
whole  and  two  quarter  cubes ;  boiler-house, 
four  quarter  cubes  ;  roof,  two  quarter  cubes  ; 
13'',  ground  plan. 

14.  Chapel,  with  Hermitage. 

15.  Two  Garden  Houses,  with  Rows  of 
Trees. 

16.  A  Castle.     16',  ground  plan. 

17.  Cloister  in  Ruins.   17",  ground  plan. 

18.  City  Gate,  with  Three  Entrances.  i8% 
ground  plan. 

19.  Arsenal.     19',  ground  plan. 

20.  City  Gate,  with  Two  Guard-Houses. 
2o",  ground  plan. 

21.  A  Monument.  21*,  ground  plan;  first 
row,  nine  whole  and  four  half  cubes  ;  second 
to  fourth  row,  each,  four  whole  cubes ;  on 
either  side,  two  quarter  cubes,  united  to  a 
square  column,  and  to  unite  the  four  columns, 
four  quarter  cubes. 

22.  A  Monument.  22*,  ground  plan  ;  first 
row,  nine  whole  and  four  quarter  cubes  ;  sec- 
ond row,  five  whole  and  four  half  cubes  ;  third 
row,  four  whole  cubes ;  fourth  row,  four  half 
cubes. 

23.  A  Large  Cross.  23",  ground  plan ;  first 
row,  nine  whole  and  Tour  times  three  quarter 
cubes ;  second  row,  four  whole  cubes  ;  third 
row,  four  half  cubes. 

Tables,  chairs,  sofas,  beds,  are  the  first 
objects  the  child  builds.  They  are  the  ob- 
jects with  which  it  is  most  familiar.     Then 


the  child  builds  a  house,  in  which  it  lives, 
speaking  of  kitchen,  sleeping  room,  parlor, 
and  eating-room,  when  representing  it.  Soon 
the  realm  of  its  ideas  widens.  It  roves  into 
garden,  street,  &c.  It  builds  the  church,  the 
school  house,  where  the  older  brothers  and 
sisters  are  instructed ;  the  factory,  arsenal, 
from  which,  at  noon  and  after  the  day's  work 
is  over,  so  many  laborers  walk  out  to  their 
homes,  to  eat  their  dinner  and  supper,  to 
rest  from  their  work,  and  to  play  with  their 
little  children.  The  ideas  which  the  children 
receive  of  all  these  objects  by  this  occupa- 
tion, grow  more  correct  by  studying  them  in 
their  details,  where  they  meet  with  them  in 
reality.  In  all  this  they  are,  as  a  matter 
of  course,  to  be  assisted  by  the  instructive 
conversation  of  the  teacher.  It  is  not  to  be 
forgotten  that  the  teacher  may  influence  the 
minds  of  the  children  very  favorably,  by  re- 
lating short  stories  about  things  and  persons 
in  connection  with  the  object  represented. 
Not  their  minds  alone  are  to  be  disciplined  ; 
their  hearts  are  to  be  developed,  and  each 
beautiful  and  noble  feeling  encouraged  and 
strengthened. 

Be  it  lemembered  again  that  it  is  not  neces- 
sary that  the  teacher  should  always  follow  the 
course  of  development  shown  in  the  pictures 
on  our  plates.  Every  course  is  acceptable, 
if  only  destruction  is  prevented  and  re-build- 
ing adhered  to.  Some  of  the  pictures  may 
not  be  familiar  to  some  of  the  children.  The 
one  has  never  seen  a  oastle  or  a  city  gate, 
a  well  or  a  monument.  Short  descriptive 
stories  about  such  objects  will  introduce  the 
child  into  a  new  sphere  of  ideas,  and  stimu- 
late the  desire  to  see  and  hear  more  and 
more,  thus  adding,  daily  and  hourly,  to  the 
stock  of  knowledge  of  which  he  is  already 
possessed.  Thus,  these  plays  will  not  only 
cultivate  the  manual  dexterity  of  the  child, 
develop  his  eye,  excite  his  fantasy,  strengthen 
his  power  of  invention,  but  the  accompanying 
oral  illustrations  will  also  instruct  him,  and 
create  in  him  a  love  for  the  good,  the  noble, 
the  beautiful. 


24 


GUIDE  TO  KINDER  GARTNERS. 


The  Fifth  Gift  is  used  with  children  from 
five  to  six  years  old,  who  are  expected  to  be 
in  their  third  3'ear  in  the  Kinder-Garten. 

A  box,  with  its  contents,  stands  on  the 
table  before  each  child.  They  empty  the 
box,  as  heretofore  described,  so  that  the  bot- 
tom row  of  the  cube,  containing  the  half  and 
quaiter  cubes,  is  made  the  top  row. 

"  What  have  you  now  ? " 

"A  cube." 

"  We  will  build  a  church.  Take  off  all 
quarter  and  half  cubes,  and  place  them  on 
the  table  before  you  in  good  order.  Move 
the  three  whole  cubes  of  the  upper  row 
together,  so  that  they  are  all  to  the  left  of 
the  other  cubes.  Take  three  more  whole 
cubes  from  the  right  side,  and  put  them  be- 
side the  three  cubes  which  were  left  of  the 
upper  row.  Take  the  three  remaining  cubes, 
which  were  on  the  right  side,  and  add  them 
to  the  quarter  and  half  cubes.  What  have 
you  now  ? " 

"  A  house  without  roof,  three  cubes  high, 
three  cubes  long,  and  two  cubes  broad." 

"  We  will  now  make  the  roof.  Place  on 
each  of  the  six  upper  cubes  a  quarter  cube 
with  its  largest  side.  Fill  up  the  space  be- 
tween each  two  quarter  cubes  with  another 
quarter  cube,  and  place  another  quarter  cube 
on  top  of  it.     What  have  you  now  ? " 

"  A  house  with  roof" 

"  How  many  cubes  are  yet  remaining  ? " 

"  Three  whole  and  six  half  cubes." 

"  Take  the  whole  cubes,  and  place  them, 
one  on  top  of  the  other,  before  the  house. 
Add  another  cube,  made  of  two  half  cubes, 
and  cover  the  top  with  half  a  cube  for  a  roof. 
What  have  you  now  ?  " 
'    "  A  steeple." 

'■  We  will  employ  the  remaining  three  half 
cubes  to  build  the  entrance.  Take  two  of  the 
half  cubes,  form  a  whole  cube  of  theni,  and 
place  it  on  the  other  side  of  the  house,  op- 
posite the  steeple,  and  lay  upon  it  the  last 
half  cube  as  a  roof.  What  have  we  built 
now  ? " 

"  A  church,  with  steeple  and  entrance." 


FORMS  OF  BEAUTY. 

If  we  consider  that  the  Fifth  Gift  is  put 
into  the  hands  of  pupils  when  they  have 
reached  the  fifth  year,  with  whom,  conse- 
quently, if  they  have  been  treated  rationally, 
the  external  organs,  the  limbs,  as  well  as  the 
senses,  and  the  bodily  mediators  of  all  men- 
tal activity,  the  nerves,  and  their  central  organ, 
the  brain,  have  reached  a  higher  degree  of 
development  and  their  physical  powers  have 
kept  pace  with  such  development,  we  may 
well  expect  a  somewhat  more  extensive  activ- 
ity of  the  pupils  so  prepared,  and  be  justified 
in  presenting  to  them  work  requiring  more 
skill  and  ingenuity  than  that  of  the  previous 
Gifts. 

And,  in  fact,  the  progress  with  these  forms 
is  apparently  much  greater  than  with  the 
forms  of  life  ;  because  here  the  importance 
of  each  of  the  thirty-nine  parts  of  the  cube 
can  be  made  more  prominent.  He  who  is 
not  a  stranger  in  mathematics  knows  that  the 
number  of  combinations  and  permutations  of 
thirtv  nine  different  bodies  does  not  count  by 
hundred?,  nor  can  be  expressed  by  thousands; 
but  thdt  millions  hardly  sullfice  to  exhaust  all 
possible  combinations. 

Limitations  are,  therefore,  necessary  here  ; 
and  these  limitations  are  presented  to  us  in 
the  laws  of  beauty,  according  to  which  the 
whole  structure  is  not  only  to  be  formed  har- 
moniously in  itself,  but  each  main  part  of  it 
must  also  answer  the  claims  of  symmetry. 
In  order  to  comply  with  these  conditions,  it 
is  sometimes  necessary,  during  the  process 
of  building  a  Form  of  Beauty,  to  perform 
certain  movements  with  various  parts  simul- 
taneously. In  such  cases  it  appears  advis- 
able to  divide  the  activity  in  its  single  parts, 
nnd  allow  the  child's  eye  to  rest  on  these 
transition  figures,  that  it  may  become  perfectly 
conscious  of  all  changes  and  phases  during 
the  process  of  development  of  the  form  in 
question.  This  will  render  more  intelligible 
to  the  young  mind,  that  real  beauty  can  only 
be  produced  when  one  opposite  balances 
another,  if   the   proportions  of  all    parts  are 


GUIDE   TO    KINDER-GARTNERS. 


25 


equally  regulated  by  uniting  them  with  one 
common  center. 

Another  limitation  we  find  in  the  fact,  that 
each  fundamental  form  from  which  we  start 
is  divided  in  two  main  parts — the  internal 
and  the  external— and  that  if  we  begin  the 
changes  or  mutations  with  one  of  these  oppo- 
sites,  they  are  to  be  continued  with  it  until  a 
certain  aim  be  reached.  By  this  process  cer- 
tain small  series  of  building  steps  are  created, 
which  enable  the  child — and,  still  more,  the  i 
teacher — to  control  the  method  according  to 
which  the  perfect  form  is  reached. 

''  Each  definite  beginning  conditions  a  cer- 
tain process  of  its  own,  and  however  much 
liberty  in  regard  to  changes  may  be  allowed, 
they  are  always  to  be  introduced  within  cer- 
tain limits  only." 

Thus,  the  fundamental  form  conditions  all 
the  changes  of  the  whole  following  series. 
All  fundamental  forms  are  distinct  from  each 
other  by  their  different  centers,  which  may  be 
a  square,  (Plate  XII.,  Fig.  9,)  a  triangle, 
(Plate  XIV.,  Fig.  37,)  a  hexagon,  octagon,  or 
circle. 

Before  the  real  formation  of  figures  com- 
mences, the  child  should  become  acquainted 
with  the  combinations  in  which  the  new  forms 
of  the  divided  cubes  can  be  brought  with 
each  other.  It  takes  two  half  cubes,  forms 
of  them  a  whole,  and,  being  guided  by  the 
law  of  opposites,  arrives  at  the  forms  repre- 
sented on  Plate  XII. — i  to  8,  and  perhaps  at 
others  of  less  significance. 

The  series  of  figures  on  Plates  XIII.,  XIV., 
XV.,  are  all  developed,  one  from  another,  as 
the  careful  observer  will  easily  detect.  As  it 
would  lead  too  far  to  show  the  gradual  grow- 
ing of  one  from  another,  and  all  from  a  com- 
mon fundamental  form,  we  will  show  only  the 
course  of  development  of  Figures  9  to  14,  on 
Plate  XII. 

The  fundamental  form  (Fig.  9)  is  a  stand- 
ing square,  formed  of  nine  cubes,  and  sur- 
rounded by  four  equilateral  triangles. 

The  course  of  development  starts  from  the 
center  part.     The  four  cubes  a  move  exter- 


nally, (Fig.  10,)  the  four  cubes  b  do  the  same, 
(Fig.  II,)  cubes  a  move  farther  to  the  corner 
of  the  triangles,  (Fig.  12,)  cubes  b  move  to 
the  places  where  cubes  a  were  previously, 
(Fig.  13.)  If  all  eight  cubes  continue  their 
way  in  the  same  manner,  we  next  obtain  a 
form  in  which  a  and  b  remain  with  their  cr " 
ners  on  the  half  of  the  catheti ;  then  follows 
a  figure  like  13,  different  only  in  so  far  as  a 
and  b  have  exchanged  positions ;  then,  in 
like  manner,  follow  12,  11,  10,  and  9. 

We,  therefore,  discontinue  the  course.  The 
internal  cubes  so  far  occupied  positions  that 
b  and  c  turned  corners,  a  and  c  sides  towards 
each  other.  In  Fig.  14,  the  opposite  appears, 
b  and  c  show  each  other  sides,  a  and  c  cor- 
ners. Thus,  in  Fig.  15,  we  reach  a  new 
fundamental  form.  Here,  not  the  cubes  of 
the  internal,  but  those  of  the  external  tri- 
angles furnish  the  material  for  changing  the 
form. 

It  is  not  necessary  that  the  teacher,  by 
strictly  adhering  to  the  law  of  development, 
return  to  the  adopted  fundamental  form.  She 
may  interrupt  the  course,  as  we  have  done, 
and  continue  according  to  new  conditions. 
But  however  useful  it  may  be  to  leave  free 
scope  to  the  child's  own  fantasy,  we  should 
never  lose  sight  of  Froebel's  principle,  to  lead 
to  lawful  action,  to  accustom  to  following  a 
definite  rule.  Nor  should  we  ever  forget  that 
the  child  can  only  derive  benefit  from  its 
occupation,  if  v,e  do  not  over-tax  the  measure 
of  its  strength  and  ability.  The  laws  of  for- 
mation should,  therefore,  always  be  as  definite 
and  distinct  as  simple.  As  soon  as  the  child 
cannot  trace  back  the  way  in  which  you  have 
led  it,  in  developing  any  of  the  forms  of  life 
or  beauty ;  if  it  cannot  discover  how  it  arrived 
at  CI  certain  point,  or  how  to  proceed  from  it, 
the  moment  has  arrived  when  the  occupation 
not  only  ceases  to  be  useful,  but  commences 
to  be  hurtful,  and  we  should  always  studiously 
avoid  that  moment. 

In  order  to  facilitate  the  child's  control  of 
his  activity,  it  is  well  to  give  the  cubes,  which 
are,  so  to  say,  the  representatives  of  the  law 


2b 


GUIDE   TO    KINDER-GARTNERS. 


of  development,  instead  of  the  letters  a,  b,  c, 
names  of  some  children  present,  or  of  friends 
of  the  pupils.  This  enlivens  the  interest  in 
their  movements,  and  the  children  follow  them 
with  much  more  attention. 

FORMS   OF   KNOWLEDGE. 

(plates  XV.  AND   XVI.) 

The  representations  of  the  forms  of  knowl- 
edge, to  which  the  Fifth  Gift  offers  oppor- 
tunity, is  of  great  advantage  for  the  develop- 
ment of  the  child.  To  superficial  observers, 
it  is  true,  it  may  appear  as  if  Froebel  not 
only  ascribed  too  much  importance  to  the 
mathematical  element  to  the  disadvantage 
of  others,  but  that  mathematics  necessarily 
require  a  greater  maturity  of  understanding 
than  could  be  found  with  children  of  the 
Kinder-Garten  age.  But  who  thinks  of  in- 
troducing mathematics  as  a  science  ?  Many 
a  child,  five  or  six  years  of  age,  has  heard 
that  the  moon  revolves  around  the  earth,  that 
a  locomotive  is  propelled  by  steam,  and  that 
lightning  is  the  effect  of  electricity.  These 
astronomical,  dynamic  and  physical  facts  have 
been  presented  to  him,  as  mathematical  facts 
are  presented  to  his  observation  in  Froebel's 
Gifts.  Most  assuredly  it  would  be  folly,  if  one 
would  introduce  in  the  Kinder-Garten  math- 
ematical problems  in  the  usual  abstract  man- 
ner. In  the  Kinder  Garten,  the  child  beholds 
the  bodily  representation  of  an  expressed 
truth,  recognizes  the  same,  receives  it  without 
difficulty,  without  overtaxing  its  developing 
mind  in  any  manner  whatsoever.  Whatever 
would  be  difficult  for  the  child  to  derive  from 
the  mere  word,  nay,  which  might  under  cer- 
tain circumstances  be  hurtful  to  the  young 
mind,  is  taught  naturally  and  in  an  easy  man- 
ner by  the  forms  of  knowledge, which  thus 
become  the  best  means  of  exercising  the 
child's  power  of  observation,  reasoning,  and 
judging.  Beware  of  all  problems  and  ab- 
stractions. The  child  builds,  forms,  sees, 
observes,  compares,  and  then  expresses  the 
truth  it  has  ascertained.  By  repetition,  these 
truths,  acquired  by  the  observation  of  facts, 


become  the  child's  mental  property,  and  this 
is  not  to  be  done  hurriedly,  but  during  the 
last  two  years  in  the  Kinder-Garten  and 
afterwards  in  the  Primary  Department. 

The  first  seven  forms  of  knowledge  on 
Plate  XV.  show  the  regular  divisions  of  the 
cube  in  three,  nine  and  twenty-seven  parts. 
In  either  case,  a  whole  cube  was  employed, 
and  yet  the  forms  produced  by.  division  are 
different.  This  shows  that  the  contents  may 
be  equal,  when  forms  are  different  (Figs.  2,  3, 
4,  or  5  and  6). 

This  difference  becomes  still  more  obvious 
if  the  three  parts  of  Fig.  2,  are  united  to  a 
standing  oblong  or  those  of  Fig.  3  to  a  lying 
oblong,  or  if  a  single  long  beam  is  formed  of 
Fig.  4. 

Take  a  cube,  children,  place  it  before  you, 
and  also  a  cube  divided  in  two  halves,  and 
place  the  two  halves  with  their  triangular 
planes  or  sides,  one  upon  another. 

These  two  halves  united  are  just  as  large 
as  the  whole  cube. 

But  the  two  halves  may  be  united,  also,  in 
other  ways.  They  may  touch  each  other  with 
their  quadratic  and  right  angular  planes. 

Represent  these  different  ways  of  uniting 
the  two  halves  of  the  cube  simultaneously. 
Notwithstanding  the  difference  in  the  forms, 
the  contents  of  mass  of  matter  remained  the 
same. 

In  a  still  more  multiform  manner,  this  fact 
may  be  illustrated  with  the  cubes  divided  in 
four  parts.  Similar  exercises  follow  now  with 
the  whole  Gift,  and  the  children  are  led  to 
find  out  all  possible  divisions  in  two,  three, 
four,  five,  nine  and  twelve  equal  parts  (Figs. 
8  to  18). 

After  each  such  division  the  equal  parts 
are  to  be  placed  one  upon  another,  for  divid- 
ing and  separating  are  always  to  be  followed 
by  a  process  of  combining  and  re-uniting. 
The  child  thus  receives  every  time,  a  trans- 
formation of  the  whole  cube,  representing  the 
same  amount  of  matter  in  various  forms 
(Fig.  19-22).  The  child  should  also  be  al- 
lowed to  compare  with  each  other  the  various 


GUIDE  TO   KINDER-GARTNERS. 


27 


thirds,  quarters,  or  sixths,  into  which  whole 
cubes  can  be  divided,  as  shown  in  Figs,  g, 
10,  II,  12,  or  14,  15  and  16. 

It  is  understood  that  all  these  exercises 
should  be  accompanied  by  the  living  word 
of  the  teacher ;  for  thereby,  only,  will  the 
child  become  perfectly  conscious  of  the  ideas 
received  from  perception,  and  the  opportunity 
is  offered  to  perfect  and  multiply  them.  The 
teacher  should,  however,  be  carefuf  not  to 
speak  too  much,  for  it  is  only  necessary  to 
keep  the  attention  of  the  pupil  to  the  object 
represented,  and  to  render  impressions  more 
vivid. 

The  divisions  introduced  heretofore,  are 
followed  by  representations  of  regular  mathe- 
matical figures,  (planes,)  as  shown  in  Figs. 
23-26.  The  manner  in  which  one  is  formed 
from  the  preceding  one  is  easily  seen  from 
the  figures  themselves. 

As  mentioned  before,  part  of  the  occupa- 
tion described  in  the  preceding  pages,  is  to 


be  introduced  in  the  Primary  Department 
only,  where  it  is  combined  with  other  inter- 
esting but  more  complicated  exercises.  Sim- 
ply to  indicate  how  advantageously  this  Gift 
may  be  used  for  instruction  in  geometry  in 
later  years,  we  have  added  the  Figs.  30*  and 
30^  the  representation  of  which  shows  the 
child  the  visible  proof  of  the  well-known 
Pythagorean  axiom,  by  which  the  theoreticai 
abstract  solution  of  the  same,  certainly,  can 
alone  be  facilitated. 

For  the  continuation  of  the  exercises  in 
arithmetic,  begun  with  the  previous  Gifts,  the 
cubes  of  the  present  one  are  of  great  use. 
Exercises  in  addition  and  subtraction  are  con- 
tinued more  extensively,  and  by  the  use  of 
these  means,  the  child  will  be  enabled  to 
learn,  what  is  usually  called  the  multiplication 
table,  in  a  much  shorter  time  and  in  a  much 
more  rational  way  than  it  could  ever  be  ac- 
complished by  mere  memorizing,  without  visi- 
ble objects. 


THE   SIXTH    GIFT. 

LARGE  CUBE,  CONSISTING   OF   DOUBLY   DIVIDED   OBLONGS. 

(plates      XVII.     to      XX.) 


As  the  Third  and  Fifth  Gifts  form  an 
especial  sequence  of  development,  so  the 
Fourth  and  Sixth  are  intimately  connected 
with  each  other.  The  latter  is,  so  to  say,  a 
higher  potence  of  the  former,  permitting,  the 
observation  in  greater  clearness,  of  the  quali- 
ties, relations,  and  laws,  introduced  previously. 

The  Gift  contains  twenty-seven  oblong 
blocks  or  bricks,  of  the  same  dimensions  as 
those  of  the  Fourth  Gift.  Of  these  twenty- 
seven  blocks,  eighteen  are  whole,  six  are 
divided  breadthwise,  each  in  two  squares, 
and  three  by  a  lengthwise  cut,  each  in  two 
columns ;  altogether  making  thirty-six  pieces. 


The  children  soon  become  acquainted  with 
this  Gift,  as  the  variety  of  forms  is  much  less 
than  in  the  preceding  one,  where,  by  an  ob- 
lique division  of  the  cubes,  an  entirely  new 
radical  principle  was  introduced. 

It  is  here,  therefore,  mainly  the  proportions 
of  size  of  the  oblongs,  squares,  and  columns 
contained  in  this  Gift  and  the  number  of  each 
kind  of  these  bodies,  about  which  the  child 
has  to  become  enlightened,  before  engaging 
in  building — playing,  creating — with  this  new 
material. 

The  cube  is  placed  upon  the  table — all  parts 
are   disjoined — then   equal    parts    collected 


28 


GUIiJE  TO   KINDER-GARTNERS. 


into  groups,  and  the  child  is  then  asked, 
"How  many  blocks  have  you  altogether?" 
How  many  oblongs?  how  many  squares? 
how  many  columns  ?  Compare  the  sides  of 
the  blocks  with  another — take  an  oblong — 
how  many  squares  do  you  need  to  cover  it  ? 
how  many  columns  ? 

Place  the  oblong  upon  its  long  edge,  now 
upon  its  shortest  side — and  state  how  many 
squares  or  columns  you  need  in  order  to 
reach  its  height,  in  either  case.  Exercises  of 
this  kind  will  instruct  the  child  sufficiently, 
to  allow  it  to  proceed,  in  a  short  time,  to  the 
individual  creating,  or  producing  occupation 
with  this  new  Gift. 

FORMS   OF   LIFE. 

(plates   XVII.  AND    XVIII.) 

It  is  the  forms  of  life,  particularly,  for 
which  this  Gift  provides  material,  far  better 
fitted,  than  any  previously  used.  The  ob- 
longs admit  of  a  much  larger  extension  of 
the  plane,  and  allow  the  enclosure  of  a  much 
more  extensive  hollow  space,  than  was  possi- 
ble, for  instance,  with  the  cubes  of  the  Fifth 
Gift.  Innumerable  forms  can  therefore  be 
produced  with  this  Gift,  and  the  attention  and 
interest  of  the  pupil  will  be  constantly  in- 
creased. 

This  very  variety,  however,  should  induce 
the  careful  teacher  to  prevent  the  child's 
purely  accidental  production  of  forms.  It  is 
always  necessary  to  act  according  to  certain 
rules  and  laws,  to  reach  a  certain  aim.  The 
established  principle,  that  one  form  should  al- 
ways be  derived  from  another,  can  be  carried 
out  here  only  with  great  difficulty,  owing  to 
the  peculiarity  of  the  material.  It  is  therefore 
frequently  necessary,  particularly  with  the 
more  complicated  structures,  to  lay  an  entirely 
new  foundation  for  the  building  to  be  erected. 

It  is  necessary,  at  all  times,  to  follow  the 
child  in  his  operations, — his  questions  should 
always  be  answered  and  suggestions  made  to 
enlarge  the  circle  of  ideas. 

It  affords  an  abundance  of  pleasure  to  a 
child  to  observe  that  we  understand  it  and 


its  work ;  it  is,  therefore,  a  great  mistake  in 
education  to  neglect  to  enter  fully  into  the 
spirit  of  the  pupil's  sphere  of  thinking  and 
acting;  and  if  we  ever  should  allow  our- 
selves to  go  so  far  as  to  ridicule  his  pro- 
ductions, instead  of  assisting  him  to  improve 
OF  them,  we  would  certainly  commit  a  most 
fatal  error. 

The  selections  of  forms  of  life  on  Plates 
XVII.  and  XVIII.,  nearly  all  of  which  are 
in  the  meantime  forms  of  art  and  knowledge, 
because  of  their  architectural  fundamental 
forms,  and  the  mathematical  proportions  of 
their  single  parts,  can,  therefore,  not  fail  to 
give  nourishment  to  various  powers  of  the 
mind, 

1.  House  without  roof;  back  wall  has  no 
door.     1%  ground  plan. 

2.  Colonnad*^  :  lowest  row,  five  oblongs 
laid  lengthwise,  and  back  wall  consisting  of 
ten  standing  oblongs,  upon  which  ten  squares. 
2',  ground  plan. 

3.  Hall,  with  columns. 

4.  Summer  House.  4%  ground  plan ;  ves- 
tibule formed  by  six  columns. 

5.  Memorial  Column  of  the  Three  Friends 
5",  ground  plan. 

6.  Monument  in  Honor  of  Some  Fallen 
Hero.  6%  ground  plan;  lowest  row,  eight 
oblongs ;  second  square  of  nine  squares,  par- 
tially constructed  of  oblongs ;  third,  four  sin- 
gle squares  ;  then  four  columns,  four  single 
squares,  square  of  nine  squares,  square  of 
four  squares,  etc. 

7.  Facade  of  a  Large  House.  7*,  ground 
plan. 

8.  The  Columns  of  the  Three  Heroes. 
8%  ground  plan. 

9.  Entrance  to  Hall  of  Fame.  9',  ground 
plan ;  first  row,  six  squares  and  six  oblongs  ; 
second  row,  six  oblongs ;  third  row,  six 
squares,  etc. 

10.  Two  Story  House,  with  yard.  10", 
ground  plan.     10'',  side  view. 

11.  Facade.     ii%  groi-nd  plan. 

12.  Covered  Summer  House.  12*,  ground 
plan. 


GUIDE    TO   KINDER-GARTNERS. 


29 


13.  Front  View  of  s>  Factory.  13*,  ground 
plan.     I3^  side  view. 

14.  Double  Colonnade.      14*,  ground  plan. 

15.  An  Altar.     15*,  ground  plan. 

16.  Monument.     16",  ground  plan. 

17.  Columns  of  Concord.  17%  ground 
plan. 

The  fantasy  pf  the  child  is  inexhaustibly 
rich  in  inventing  new  forms.  It  creates  gar- 
dens, yards,  stables  with  horses  and  cattle, 
household  furniture  of  all  kinds,  beds  with 
sleeping  brothers  and  sisters  in  them,  tables, 
chairs,  sofas,  etc,  etc. 

If  several  children  combine  their  individual 
building  they  produce  large  structures,  perfect 
barn-yards  with  all  out-buildings  in  them,  nay, 
whole  villages  and  towns.  The  ideas  that  in 
union  there  is  strength,  and  that  by  co-oper- 
ation great  things  may  be  accomplished,  will 
thus  early  become  manifest  to  the  young 
mind. 

FORMS  OF  BEAUTY. 

(plates   XIX.  AND  XX.) 

The  forms  of  beauty  of  this  Gift  offer  far  less 
diversity  than  those  of  Gift  No.  5 ;  owing,  how- 
ever, to  the  peculiar  proportions  of  the  plane, 
they  present  sufficient  opportunity  for  charac- 
teristic representations,  not  to  be  neglected. 

We  give  on  the  accompanying  plates  a  sin- 
gle succession  of  development  of  such  forms. 
The  progressive  changes  are  easily  recog- 
nized, as  the  oblong,  which  needs  to  be  moved 
to  produce  the  following  figure,  is  always 
marked  by  a  letter.  The  center-piece  always 
confiists  of  two  of  the  little  columns,  standing 
one  upon  another,  and  important  modifica- 


tions may  be  produced  by  using  the  oblongs 
in  lying  or  standing  positions.  By  employing 
the  four  little  columns  in  various  ways,  many 
pleasant  changes  can  be  produced  by  them. 

FORMS   OF   KNOWLEDGE. 

(plate   XX.) 

These  also  appear  in  much  smaller  num- 
bers compared  with  the  richness  and  multi- 
plicity of  the  Fifth  Gift.  By  the  absence  of 
oblique  (obtuse  and  acute)  angles,  they  are 
limited  to  the  square  and  oblong,  and  exer- 
cises introduced  with  these  previously,  may 
be  repeated  here  with  advantage. 

All  Froebel's  Gifts  are  remarkable  for  the 
peculiar  feature  that  they  can  be  rendered  ex- 
ceedingly instructive  by  frequently  introduc- 
ing repetitions  under  varied  conditions  and 
forms,  by  which  means  we  are  sure  to  avoid 
that  dry  and  fatiguing  monotony  which  must 
needs  result  from  repeating  the  same  thing  in 
the  same  manner  and  form.  And  still  more, 
the  child,  thereby,  becomes  accustomed  to 
recognize  like  in  unlike,  similarity  in  dissimi- 
larity, oneness  in  multiplicity,  and  connection 
in  the  apparently  disconnected. 

In  Fig.  16-22,  all  squares  that  can  be 
formed  with  the  Sixth  Gift  are  represented. 
In  Fig.  23  we  see  a  transition  from  the  forms 
of  knowledge  to  those  of  beauty. 

With  the  Sixth  Gift  we  reach  the  end  of 
the  two  series  of  development  given  by 
Froebel  in  the  building  blocks,  whose  aim 
is  to  acquaint  the  child  with  the  general 
qualities  of  the  solid  body  by  own  observa- 
tion and  occupation  with  the  same. 


THE  SEVENTH  GIFT. 
SQUARE  AND    TRIANGULAR  TABLETS   FOR  LAYING  OF  FIGURES. 

(plates    XXI.   TO    XXIX.) 


All  mental  development  begins  with  con- 
crete beings.  The  material  world  with  its 
multiplicity  of  manifestations  first  attracts 
the  senses  and  excites  them  to  activity,  thus 
causing  the  rudimental  operations  of  the 
mental  powers.  Gradually—only  after  many 
processes,  little  defined  and  explained  by  any 
science  as  yet,  have  taken  place— man  be- 
comes enabled  to  proceed  to  higher  mental 
activity,  from  the  original  im'pressiorts  made 
upon  his  senses  by  the  various  surroundings 
in  the  material  world. 

The  earliest  impressions,  it  is  true,  If  often 
repeated,  leave  behind  them  a  lasting  trace 
on  the  m.ind.  But  between  this  attained  pos- 
sibility to  recall  once-made  observations,  to 
represent  the  object  perceived  by  our  senses, 
by  mental  image  (imagination),  and  the 
real  thinking  or  reasoning,  the  real  pure  ab- 
straction, there  is  a  very  long  step,  and 
nothing  in  our  whole  system  of  education  is 
more  worthy  of  consideration  than  the  sud- 
den and  abrupt  transition  from  a  life  in  the 
concrete,  to  a  life  of  more  or  less  abstract 
thinking  to  which  our  children  are  submitted 
when  entering  school  from  the  parental 
house. 

Froebel,  by  a  long  series  of  occupation 
material,  has  successfully  bridged  over  this 
chasm,  which  the  child  has  to  traverse,  and 
the  first  place  among  it,  the  laying  tablets  of 
various  forms  occupy. 

The  series  of  tablets  is  contained  in  five 
boxes  containing— 

A.  Quadrangular  square  tablets. 


Trian- 
gular 
tablets. 


B.  Right  angular  (equal  sides). 

C.  Equilateral. 

D.  Obtuse  angular  (equal  sides). 

E.  Right  angular  (unequal  sides).  > 
The    child   was  heretofore   engaged  with 

solid  bodies,  and  in  the  representation  of 
real  things.  It  produced  a  house,  garden, 
sofa,  etc.  It  is  true  -the  sofa  was  not  a  sofa 
as  it  is  seen  in  reality ;  the  one  built  by  the 
child  was,  therefore,  so  to  say,  an  image  al- 
ready, but  it  was  a  bodily  image,  so  much  so 
that  the  child  could  place  upon  it  a  little 
something  representing  its  doll.  The  child 
considered  it  a  real  sofa,  and  so  it  was  to  the 
child,  fulfilling,  as  it  did.  in  its  litde  world, 
the  purposes  of  a  real  sofa  in  real  life. 

With  the  tablets,  the  embodied  planes,  the 
child  can  not  represent  a  sofa,  but  a  form 
similar  to  it ;  an  image  of  the  sofa  can  be  pro- 
duced by  arranghig  the  squares  and  triangles 
in  a  certain  order. 

We  shall  see,  at  some  future  time,  how 
Froebel  continues  on  this  road,  progressing 
from  the  plane  to  the  line,  from  the  line  to 
the  point,  and  finally  enables  the  child  to 
draw  the  image  of  the  object,  with  pencil  or 
pen  in  his  own  little  hand. 

A.    THE  QUADRANGULAR    LAYING   TAB- 
LETS (Squares), 
(plate  XXI ) 
They  are  given  the  child  first  to  the  num- 
ber  of  six.     In  a  simiUr  way  as  was  done 
with  the  various  building  gifts,  the  child  is 
led  to  an  acquaintance  with  the  various  quali* 


GUIDE  TO   KINDER-GARTNERS. 


31 


ties  of  the  new  material,  and  to  compare  it, 
with  other  things,  possessing  similar  qualities. 
It  is  advisable  to  let  the  child  understand 
the  connection  existing  between  this  and  the 
previous  gifts.  The  laying  tablets  are  nothing 
but  the  embodied  planes,  or  separated  sides 
of  the  cube.  Cover  all  the  sides  of  a  cube 
with  square  tablets  and  after  the  child  has 
recognized  the  cube  in  the  body  thus  formed, 
let  it  separate  the  tablets  one  by  one,  from 
the  cube  hidden  by  them. 

The  following,  or  similar  questions  are  here 
to  be  introduced : — What  is  the  form  of  this 
tablet?  How  many  sides  has  it?  How 
many  angles  ?  Look  carefully  at  the  sides. 
Are  they  alike  or  unlike  each  other?  They 
are  all  alike.  Now  look  at  the  corners.  These 
also  are  all  alike.  Where  have  you  seen  sim- 
ilar figures  ? 

What  are  such  figures  called?  Can  you 
show  me  angles  somewhere  else  ?  Where 
the  two  walls  meet  is  an  angle.  Here,  there, 
and  everywhere  you  find  angles. 

But  all  angles  are  not  alike,  and  they  are 
therefore  differently  named.  All  these  dif- 
ferent names  you  will  learn  successively,  but 
now  let  us  turn  to  our  tablet.  Place  it  right 
straight  before  you  upon  the  table.  Can  you 
tell  me  now  what  direction  these  two  sides 
have  which  form  the  angle  ?  The  one  is 
horizontal,  the  other  perpendicular.  An 
angle  which  is  formed  if  a  perpendicular 
meets  a  horizontal  line,  is  called  a  right  an- 
gle. How  many  of  such  angles  can  you 
count  on  your  tablet?  Four.  Show  me  such 
right  angles  somewhere  else. 

By  the  acquisition  of  this  knowledge  the 
child  has  made  an  important  step  forward. 
Looking  for  horizontal  and  perpendicular 
lines,  and  for  right  angles,  it  is  led  to  investi- 
gate more  deeply  the  relations  of  form,  which 
it  had  heretofore  obser\'ed  only  in  regard  to 
the  size  conditioned  by  it. 

The  child's  attention  should  be  drawn  to 
the  fact  that,  however  the  tablet  may  be 
placed  the  angles  always  remain  right  angles 
though  the  lines   are  horizontal  and  perpen- 


dicular only  in  four  positions  of  the  tablet, 
namely,  those  where  the  edges  of  the  tablet 
are  placed  in  the  same  direction  with  the 
lines  on  the  table  before  the  child.  This 
will  give  occasion  to  lead  the  child  to  a  gen- 
eral perception  of  the  standing  or  hanging  of 
objects  according  to  the  plummet. 

But  the  tablet  will  force  still  another  ob- 
servation upon  the  child.  The  opposite  sides 
have  an  equal  direction  ;  they  are  the  same 
distance  from  each  other  in  all  their  points ; 
they  never  meet,  however  many  tablets  the 
child  may  add  to  each  other  to  form  the  lines. 

The  child  learns  that  such  lines  are  called* 
parallel  lines.  It  has  observed  such  lines 
frequently  before  this,  but  begins  just  now  to 
understand  their  real  being  and  meaning. 
It  looks  now  with  much  more  interest  than 
ever  before  at  surrounding  tables,  chairs, 
closets,  houses,  with  their  straight  line  orna- 
ments, for  now  the  little  cosmopolitan  does 
not  only  receive  the  impressions  made  by  the 
surroundings  upon  his  senses,  but  he  already 
looks  for  something  in  them,  an  idea  of  which 
lives  in  his  mind.  Although  unconscious  of 
the  fact  that  with  the  right  angle  and  the 
parallel  line,  he  received  the  elements  of 
architecture,  it  will  pleasantly  incite  him  to 
new  observations  whenever  he  finds  them 
again  in  another  object  which  attracts  his 
attention. 

The  teacher  in  remembrance  of  our  oft- 
repeated  hints,  will  proceed  slowly,  and  care- 
fully, according  to  the  desire  and  need  of  the 
child.  She  repeats,  explains,  leads  the  child 
to  make  the  same  observations  in  the  most 
different  objects,  and  changing  circumstances, 
or  guides  the  child  in  laying  other  forms  of 
knowledge  (lying  or  standing  parallelograms 
Fig.  4  and  5)  of  life,  (steps,  Fig.  6  and  8, 
double  steps,  Fig.  7  and  9,  door.  Fig.  10,  sofa, 
Fig.  II,  cross,  Fig.  12),  or  forms  of  beauty. 

The  number  of  these  forms  is  on  the  whole 
only  very  limited.  It  is  well  now  to  augment 
the  number  of  tablets  in  the  hands  of  the 
pupil,  by  two,  when  a  much  larger  number  of 
forms  can  be  produced.     The  various  series 


32 


GUIDE  TO   KINDER-GARTNERS. 


of  forms  of  beauty,  introduced  with  the  third 
Gift,  can  be  repeated  here  and  enlarged  upon, 
according  to  the  change  in  the  material  now 
at  the  disposal  of  the  child. 

B.     RIGHT-ANGLED  TRIANGLES. 

(plate    XXI   ) 

As  from  the  whole  cube,  the  divided  cube 
was  produced,  so  by  division  the  triangle 
springs  from  the  square.  By  dividing  it 
diagonally  in  halves,  we  produce  the  rectan- 
gular triangle  with  equal  sides. 

Although  the  form  of  the  triangle  was  pre- 
•sented  to  the  child  in  connection  with  the 
Fifth  Gift,  it  here  appears  more  independently, 
and  it  is  not  only  on  that  account  necessary 
to  acquaint  the  child  with  the  qualities  and 
being  of  the  new  addition  to  its  occupation 
material,  but  still  more  so  as  the  forms  of 
the  triangles  with  which,  as  a  natural  sequence 
it  will  have  to  do  hereafter,  were  entirely 
unknown  to  the  pupil.  The  child  places  two 
triangles,  joined  to  a  square,  upon  the  table. 

What  kind  of  a  line  divides  your  four-cor- 
nered tablet?  An  oblique  or  slanting  line. 
In  what  direction  does  the  line  cut  your 
square  in  two  ?  From  the  right  upper  corner 
to  the  left  lower  corner.  Such  a  line  we  call 
a  diagonal. 

Separate  the  two  parts  of  the  square,  and 
look  at  each  one  separately.  What  do  you 
call  each  of  these  parts  ?  What  did  you  call 
the  whole  ?  A  square.  How  many  corners 
or  angles  had  the  square  ?  Four.  How  many 
corners  or  angles  has  the  half  of  the  square 
you  are  looking  at  ?  Three.  This  half, 
therefore,  is  called  a  triangle,  because,  as  I 
have  explained  to  you  before,  it  has  three 
angles.  How  many  sides  has  your  tri- 
angle ?  etc. 

Looking  at  the  sides  more  attentively, 
what  do  you  observe  ?  One  side  is  long,  the 
other  two  are  shorter,  and  like  each  other. 
These  latter  are  as  large  as  the  sides  of  the 
square,  all  sides  of  which  were  alike. 

Now  tell  me  what  kind  of  angle  it  is,  that 
is  formed  by  these  two  equal  sides  ?     It  is  a 


right  angle.  Why?  and  what  will  you  call 
the  other  two  angles  ?  How  do  the  sides 
run  which  form  these  two  angles  ?  They  run 
in  such  a  way  as  to  form  a  very  sharp  point, 
and  these  angles  are,  therefore,  called  acute 
angles,  which  means  sharp-pointed  angles. 
Your  triangle  has  then,  how  many  different 
kinds  of  angles  ?  Two  ;  one  right  angle,  and 
two  acute  angles. 

It  is  not  necessary  to  mention  that  the 
above  is  not  to  be  taught  in  one  lesson.  It 
should  be  presented  in  various  conversations, 
lest  the  acquired  knowledge  might  not  be 
retained  by  even  the  brightest  child.  The 
attention  of  the  pupil  may  also  be  led,  in 
subsequent  conversations  to  the  fact  that  the 
largest  side  is  opposite  the  largest  angle,  and 
that  the  two  acute  angles  are  alike,  etc. 
Sufficient  opportunity  for  these  and  additional 
remarks  will  offer  itself  during  the  represen- 
tations of  forms  of  life,  of  knowledge,  and  of 
beauty,  for  which  the  child  will  employ  its 
tablets,  according  to  its  own  free  will,  and 
which  are  not  necessarily  to  be  separated, 
neither  here  nor  in  any  other  part  of  these 
occupations,  although  it  is  well  to  observe  a 
certain  order  at  any  time. 

Whenever  it  can  be  done,  elementary  knowl- 
edge may  well  be  imparted,  together  with  the 
representations  of  forms  of  life,  and  forms  of 
beauty. 

In  order  to  invent,  the  child  must  have 
observed  the  various  positions  which  a  trian- 
gle may  occupy.  It  will  find  these  acting 
according  to  the  laws  of  opposites,  already 
familiar  to  the  child. 

The  right  angle,  to  the  right  below,  (Fig.  17) 
it  will  bring  into  the  opposite  direction  to  the 
left  above,  (Fig.  18)  then  into  the  mediative 
positions  to  the  left  below,  (Fig.  19)  and  to 
the  right  above,  (Fig.  20).  By  turning,  it 
comes  above  the  long  side,  (Hypothenuse,  Fig. 
21)  then  opposite  below  it,  (Fig.  22)  then  to 
the  right,  (Fig.  23)  and  finally  to  the  left  of 
it,  (Fig.  24). 

The  various  positions  of  two  triangles  are 
easily  found  by  moving  one  of  them  around 


GUIDE  TO   KINDER-GARTNERS. 


33 


the  other.  Fig.  26-31  are  produced  from 
Fig.  25,  by  moving  the  triangle  marked  a, 
always  keeping  it  in  its  original  position, 
around  the  other  triangle. 

In  Figs.  32-37,  the  changes  are  produced, 
alternating  regularly  between  a  turn  and  a 
move  of  the  triangle  a.  In  Figs.  38-47, 
simply  turning  takes  place. 

After  the  child  has  become  acquainted  with 
the  first  elements  from  which  its  formations 
develop,  it  receives  for  a  beginning  four  of 
the  triangled  tablets.  It  then  places  the 
right  angles  together,  and  thereby  forms  a 
standing  full  square,  (Fig.  48.) 

By  placing  the  tablets  in  an  opposite  posi- 
tion, turning  the  right  angles  from  within  to 
without,  it  produces  a  lying  square  with  the 
hollow  in  the  middle,  {Fig.  49).  This  hollow 
space  has  the  same  shape  and  dimensions  as 
Fig.  48.  The  child  will  fancy  Fig.  48  into  the 
place  of  this  hollow  space,  and  will  thereby 
transfer  the  idea  of  a  full  square  upon  an 
empty  or  hollow  one,  and  will  consequently 
make  the  first  step  from  the  perception  of  the 
concrete  to  its  idea,  the  abstraction. 

The  child  will  now  easily  find  mediative 
forms  between  these  two  opposites.  It  places 
two  right  angles  within  and  two  without, 
(Fig.  58  and  59)  two  above,  and  two  below, 
(Fig.  50)  two  to  the  right,  and  two  to  the  left, 

(Fig.  51)- 

So  far,  two  tablets  always  remained  con- 
nected with  one  another.  By  separating 
them  we  produce  the  new  mediative  forms, 
52,  53,  54  and  55,  in  which  again  two  and 
two  are  opposites.  But  instead  of  the  right, 
the  acute  angles  may  meet  in  a  point  also, 
and  thus  Figs.  56  and  57  are  produced, 
which  are  called  rotation  forms,  because  the 
isolated  position  of  the  right  angle  suggests, 
as  it  were,  an  inclination  to  fall,  or  turn,  or 
rotate. 

The  mediation  between  these  two  oppo- 
site figures  is  given  in  Figs.  50  and  51 — 
between  them  and  Figs.  49  and  50  in  Figs. 
58  and  59 ;  and  it  should  be  remarked  in 
this  connection,  that  these  opposites  are  con- 
5 


ditioned  by  the  position  of  the  right  angle  in 
all  these  cases. 

All  these  exercises  accustom  the  pupil  to  a 
methodic  handling  of  all  his  material.  They 
develop  a  correct  use  of  his  eye,  because 
regular  figures  will  only  be  produced  when 
his  tablets  are  placed  correctly  and  exactly 
in  their  places  shown  by  the  net-work  on  the 
table.  The  precaution  which  must  be  exer- 
cised by  the  child  not  to  disturb  the  easily 
movable  tablets,  and  the  care  employed  to 
keep  each  in  its  place,  are  of  the  greatest 
importance  for  future  necessary  dexterity  of 
hand.  In  a  still  greater  degree  than  by  these 
simple  elementary  forms  just  described,  this 
will  be  the  case,  when  the  pupil  comes  into 
possession  of  the  following  boxes,  containing 
a  larger  number — up  to  sixty-four — tablets  for 
the  formation  of  more  complicated  figures, 
according  to  the  free  exercise  of  his  fantasy. 

FORMS   OF   LIFE. 
(plate  xxin.) 
All  hints  given  in  connection  with  the  build- 
ing blocks,  are  also  to  be  followed  here,  with 
this    difference   only,  that  we   produce   now 
images  of  objects,  whereas,   heretofore,   we 
united  the  objects  themselves. 
The  child  here  begins — 

A,  WITH    FOUR   TABLETS. 

And  forms  with  them — 
I.  A  flower-pot.     2.  A  little  garden-house. 
3.  A  pigeon-house. 

B,  WITH    EIGHT   TABLETS. 

4.  A  cottage.  5.  A  canoe  or  boat.  6. 
A  covered  goblet.  7.  A  light-house.  8.  A 
clock. 

C,  WITH    SIXTEEN   TABLETS. 

9.  A  bridge  with  two  spans.  10.  A  large 
gate.  II.  A  church.  12.  A  gate  with  bel- 
fry.    13.  A  fruit  basket. 

D,  WITH    THIRTY-TWO    TABLETS. 

14.  A  peasant's  house.  15-  A  forge  with 
high  chimney.  16.  A  coffee-mill.  17.  A  cof- 
fee-pot without  handle. 


34 


GUIDE   TO    KINDER-GARTNERS. 


E,  WITH    SIXTY-FOUR    TABLETS. 

i8.  A  two-Story  house.  19.  Entrance  to  a 
railroad  depot.     20.  A  steamboat. 

In  No.  21,  we  see  the  result  of  combined 
activity  of  many  children.  Although  to  some 
grown  persons  it  may  appear  as  if  the  images 
produced  do  not  bear  much  resemblance  to 
what  they  are  intended  to  represent,  it  should 
be  remembered  that  in  most  cases,  the  chil- 
dren themselves  have  given  the  names  to 
the  representations.  Instructive  conversation 
should  also  prevent  this  drawing  with  planes^ 
as  it  were,  from  being  a  mere  mechanical  pas- 
time ;  the  entertaining,  living  word  must  in- 
fuse soul  into  the  activity  of  the  hand  and  its 
creations.  Each  representation,  then,  will 
speak  to  the  child  and  each  object  in  the 
world  of  nature  and  art  will  have  a  story  to 
tell  to  the  child  in  a  language  for  which  it 
will  be  well  prepared. 

We  need  not  indicate  how  these  conversa- 
tions should  be  carried  on,  or  what  they 
should  contain.  Who  would  not  think,  in 
connection  with  the  pigeon  house,  of  the 
beautiful  white  birds  themselves,  and  the  nest 
they  build  ;  the  white  eggs  they  lay,  the  ten- 
der young  pigeons  coming  from  them,  and 
the  care  with  which  the  old  ones  treat  the 
young  ones,  until  they  are  able  to  take  care 
of  themselves.  An  application  of  these  re- 
lations to  those  between  parents  and  children, 
and,  perhaps,  those  between  God  and  man, 
who,  as  his  children  enjoy  his  kindness  and 
love  every  moment  of  their  lives,  may  be 
made,  according  to  circumstances  —  all  de- 
pending on  the  development  of  the  children. 
However,  care  should  always  be  taken  not  to 
present  to  them,  what  might  be  called  ab- 
stract morals,  which  the  young  mind  is  unable 
to  grasp,  and  which,  if  thus  forced  upon  it 
cannot  fail  to  be  injurious  to  moral  develop- 
ment. The  aim  of  all  education  should  be 
love  of  the  good,  beautiful,  noble,  and  sub- 
lime ;  but  nothing  is  more  apt  to  kill  this 
very  love,  ere  it  is  born,  than  the  monotony 
of  dry,  dull  preaching  of  morals  to  young 
children.      Words  not  so  much  as  deeds — 


actual  experiences  in  the  life  of  the  child,  are 
its  most  natural  teachers  in  this  important 
branch  of  education. 

FORMS  OF  BEAUTY. 

(plates    XXI.   AND    XXII.) 

Owing  to  the  larger  multiplicity  of  ele- 
mentary forms  to  be  made  with  the  triangles, 
the  number  of  Forms  of  Beauty  is  a  very  large 
one.  Triangle,  square,  right  angle,  rhomb, 
hexagon,  octagon,  are  all  employed,  and  the 
great  diversity  and  beauty  of  the  forms  pro- 
duced lend  a  lasting  charm  to  the  child's 
occupation.  Its  inventive  power  and  desire, 
led  by  law,  will  find  constant  satisfaction,  and 
to  give  satisfaction  in  the  fullest  measure 
should  be  a  prominent  feature  of  all  systems 
of  education. 

FORMS  TO  BE  BUILT  WITH  FOUR  TABLETS 

have  already  been  mentioned  on  page  33,  as 
contained  on  Plate  XXI — D,  48-59.  We  find 
more  satisfaction  by  employing 

EIGHT    TABLETS. 

In  working  with  them,  we  can  follow  th\ 
most  various  principles  Series  E,  60-69.  '^ 
formed  by  doubling  the  forms  produced  by 
four  tablets  ;  series  F,  starting  from  the  fun- 
damental form  70.  making  one  half  of  the 
tablets  move  from  kft  to  right,  the  length  of 
one  side,  with  e?ch  move.  A  new  series 
would  be  produced,  if  we  move  from  right  to 
left  in  a  similar  manner.  In  these  figures, 
sides  always  touch  sides,  and  corners  touch 
corners — consequently,  parts  of  the  same  kind. 

The  transition  or  mediation  between  these 
two  opposites,  the  touching  of  corners  and 
sides,  would  be  produced  by  shortening  the 
movement  of  the  traveling  triangle  one-half, 
permitting  ^t  to  proceed  one  half  side  only. 

But  let  us  return  to  fundamental  form  70. 
In  it,  either  large  sides  (hypothenuses)  or 
small  sides  (catheti)  constantly  touch  one 
another.  The  opposite — large  side  touching 
small — we  havq  in  Fig.  82,  and  by  traveling 
from  right  to  left  of  half  the  triangles,  series 


GUIDE   TO    KINDER-GARTNERS. 


35 


G,  82  to  87,  is  produced.  We  would  have 
produced  a  much  larger  number  of  forms,  if 
we  had  not  interrupted  progress  by  turning 
the  triangles  produced  by  Fig.  86. 

In  the  fundamental  forms  70  and  82,  the 
sides  touched  one  another.  Fig.  88  shows 
that  they  may  touch  at  the  corners  only.  In 
this  figure,  the  right  angles  are  without ;  in 
89  and  90,  they  are  within.  Fig.  90  is  the 
mediation  between  70  and  89,  for  four  tablets 
touch  with  their  sides  (70)  four  with  the  cor- 
ners (89).  No.  91  is  the  opposite  of  90,  full 
center,  (empty  center,)  and  mediation  between 
88  and  89 — (four  right  angles  without,  as  in 
88,  and  four  within,  as  in  89.)  It  is  already 
seen,  from  these  indications,  what  a  treasure 
of  forms  enfolds  itself  here,  and  how,  with 

SIXTEEN   TABLETS, 

it  again  will  be  multiplied. 

It  would  be  impossible  to  exhaust  them. 
Least  of  all,  should  it  be  the  task  of  this 
work  to  do  this,  when  it  is  only  intended  to 
show  how  the  productive  self-occupation  of 
the  pupil  can  fittingly  be  assisted.  We  be- 
lieve, besides,  that  we  have  given  a  suffi- 
cient number  of  ways  on  which  fantasy  may 
travel,  perfectly  sure  of  finding  constantly 
new,  beautiful,  eye  and  taste  developing  for- 
mations. We,  therefore,  simply  add  the  series 
J  and  K,  the  first  of  which  is  produced  by 
quadrupling  some  of  the  elementary  forms 
given  at  D,  48  to  59,  and  the  second  of  which 
indicates  how  new  series  of  forms  of  beauty 
may  be  developed  from  each  of  these  forms. 
It  must  be  evident,  even  to  the  casual  ob- 
server, how  here  also  the  law  of  opposites, 
and  their  junction,  was  observed.  Opposites 
are  92  and  93  ;  mediation,  94  and  95  :  oppo- 
sites. 96  and  97  ;  mediation,  98,  99,  and  roo: 
opposites,  loi  and  102  ;  mediation,  103,  etc. 

WITH    THIRTY-TWO   TABLETS. 

As  heretofore,  we  proceed  here  also  in  the 
same  manner,  by  multiplying  the  given  ele- 
ments, or  by  means  of  further  development, 
according  to  the  law  of  opposites.      As  an 


example,  we  give  Series  L.  the  members  of 
which  are  produced  by  a  four-fold  junction 
of  the  elements  68  and  69.  no  and  iii  are 
opposites;  112  and  113  mediative  forms. 

WITH    SIXTY-FOUR    TABLETS. 

Here,  also,  the  combined  activity  of  many 
children  will  result  in  forms  interesting  to  be 
looked  at,  not  only  by  little  children.  There 
is  another  feature  of  this  combined  activity 
not  to  be  forgotten.  The  children  are  busy 
obeying  the  same  law ;  the  same  aim  unites 
them — one  helps  the  other.  Thus  the  condi- 
tions of  human  society — family,  community, 
states,  etc, — are  already  here  shown  in  their 
efTects.  A  system  of  education  which,  so  to 
speak,  by  mere  play,  leads  the  child  to  appre- 
ciate those  requisites,  by  compliance  with 
which  it  can  successfully  occupy  its  position 
as  man  in  the  future,  certainly  deserves  the 
epithet  of  a  natural  and  rational  orie. 

Figures  114,  115,  116,  are  enlarged  pro- 
ductions from  96  and  97.  They  are  planned 
in  such  a  way,  as  to  admit  of  being  continued 
in  all  directions,  and  thus  serve  to  carry  out 
the  representation  of  a  very  large  design. 

After  having  acted  so  far,  according  to  in- 
dications made  here,  it  is  now  advisable  to 
start  from  the  fundamental  forms  presented 
in  the  Fifth  Gift,  and  to  use  them,  with  the 
necessary  modifications,  in  farther  occupying 
the  pupils  with  the  tablets.  Fig.  117  gives 
a  model,  showing  how  the  motives  of  the 
Fifth  Gift  can  be  used  for  this  purpose. 

FORMS  OF  KNOWLEDGE. 

(plate   XXII.) 

By  joining  two,  four,  and  eight  tablets,  we 
have  already  become  acquainted  with  the 
regular  figures  which  may  be  formed  with 
them,  namely,  triangle,  quadrangle  (square), 
right  angle,  rhomboid,  and  trapezium  (Plate 
XXII.,  Figs.  118-123). 

The  tablets  are,  however,  especially  quali- 
fied to  bring  to  the  observation  of  the  child 
different  sizes  in  equal  forms  (similar  figures), 
and  equal  siz^  in  different  forms. 


(sviuiL    lO    KllNUiiR  GARTNERS. 


Figures  124,  125,  and  126  show  triangles 
of  which  each  is  the  halt"  of  the  following, 
and  Nos.  129,  127.  and  128,  three  squares 
of  that  kind.  Figures  1 19-123,  and  129- 
131,  show  the  former  five,  the  latter  three 
times  the  same  size  in  different  forms. 

That  the  contemplation  of  these  figures, 
the  occupation  with  them,  must  tend  to  facili- 
tate the  understanding  of  geometrical  axioms 
in  future,  who  can  doubt?  And  who  can 
gainsay  that  mathematical  instruction,  by 
means  of  Froebel's  method,  must  needs  be 
facilitated,  and  better  results  obtained  ?  That 
such  instruction,  then,  will  be  rendered  more 
fruitful  for  practical  life,  is  a  fact  which  will 
be  obvious  to  all,  who  simply  glance  at  our 
figures,  even  without  a  thorough  explanation. 
They  contain  demonstratively  the  larger  num- 
ber of  the  axioms  in  elementary  geometry, 
which  relate  to  the  conditions  of  the  plane  in 
regular  figures. 

For  the  present  purpose,  it  is  sutiicient  if 
the  child  learns  to  distinguish  the  various  kinds 
of  angles,  if  it  knows  that  the  right  angles 
are  all  equally  large,  the  acute  angles  smaller, 
and  the  obtuse  angles  larger  than  a  right 
angle,  v/hich  the  child  will  easily  understand 
by  putting  one  upon  another.  A  deeper  in- 
sight in  the  matter  must  be  reserved  for  the 
primary  department  of  instruction. 

C.  THE  EQUILATERAL  TRL\NGLE. 

(plates   XXIV.  AND   XXV.) 

So  far  the  right  angle  has  predominated  m 
the  occupations  with  the  tablets,  and  the 
acute  angle  only  appeared  in  subordinate 
relations.  Now  it  is  the  latter  alone  which 
governs  the  actions  of  the  child  in  producing 
forms  and  figures. 

The  child  will  compare  the  equilateral 
triangle,  which  it  receives  in  gifts  of  3.  6.  9, 
and  12,  first  with  the  isosceles,  right-angled 
tablet  already  known  to  him.  Both  have  three 
sides,  both  three  angles,  but  on  close  observa- 
tion not  only  their  similarities,  but  also  their 
dissimilarities  will  become  apparent.  The 
three  angles  of  the  new  triangle «.re  all  smaller 


than  a  right  angle,  are  acute  angles  and  the 
three  sides  are  just  alike,  hence  the  name — 
equilateral — meaning  ^''  equal  sided"  triangle. 

Joining  two  of  these  equilateral  tablets  the 
child  will  discover  that  it  cannot  form  any 
of  the  regular  figures  previously  produced. 
No  triangle,  no  square,  no  right  angle,  no 
rhomboid,  can  be  produced,  but  only  a  form 
similar  to  the  latter,  a  rhomboid  with  four 
equal  sides.  To  undertake  to  produce  forms 
of  life  with  these  tablets  would  prove  very 
unsatisfactory.  Of  particular  interest,  how- 
ever, because  presenting  entirely  new  forma- 
tions, are 

THE  FORMS  OF  BEAUTY. 
The  child  first  receives  three  tablets  and 
will  find  the  various  positions  of  the  same 
towards  one  another  according  to  the  law  of 
opposites  and  their  combination.  Vide  Plate 
XXIV.,  1-9. 

SIX   TABLETS. 

The  child  will  unite  his  tablets  around  one 
common  center  (Fig.  10),  form  the  opposite 
(Fig  11),  and  then  arrive  at  the  forms  of  me- 
diation 12,  13,  14,  and  15,  or  it  unites  three 
elementary  forms  each  composed  of  two  tab- 
lets as  done  in  16,  and  forms  the  opposite 
17  and  the  mediations  18  and  19,  or  it  starts 
from  No.  10,  turning  first  i,  then  2,  then  3 
tablets,  outwardly.  By  turning  one  tablet, 
21  and  22,  by  turning  two  tablets,  23,  24,  25. 
26.  27,  28  and  29.  are  produced  from  No.  20. 
This  may  be  continued  with  3,  4,  and  5  tab- 
lets. All  forms  thus  received  give  us  ele- 
mentary forms  which  may  be  employed  as 
soon  as  a  larger  number  of  tablets  are  to  be 
used. 

NINE  TABLETS. 

As  with  the  right-angled  triangle,  small 
groups  of  tablets  were  combined  to  form 
larger  figures,  so  we  also  do  here.  The  ele- 
mentary forms  under  A  give  us  in  threefold 
combination  the  series  of  forms  under  C,  30 — 
40,  which  in  course  of  the  occupation  may  be 
multiplied  at  will. 


•i^ 


GUIDE   TO    KINDER  GARTNERS. 


n 


TWELVE   TABLETS. 
(plate  XXV.) 

Half  of  the  tablets  are  painted  brown,  the 
balance  blue  By  this  difference  in  color,  op- 
posites  are  rendered  more  conspicuous,  and 
these  twelve  tablets  thus  afford  a  splendid 
opportunity  for  illustrating  more  forcibly  the 
law  of  opposites  and  their  combination. 
Plate  XXV.  shows  how,  by  combination  of 
opposites  in  the  forms  a  and  b^  every  time 
the  star  c  is  produced.  Entirely  new  series  of 
forms  may  be  produced  by  employing  a  larger 
number  of  tablets,  i8,  24  or  36.  We  are, 
however,  obliged  to  leave  these  representa- 
tions to  the  combined  inventive  powers  of 
teacher  and  pupil, 

FORMS   OF   KNOWLEDGE. 

It  has  been  mentioned  before,  that  the 
previously  introduced  regular  mathematical 
figures  do  not  appear  here  as  a  whole.  How- 
ever, a  triangle  can  be  represented  by  four  or 
nine  tablets,  a  rhomboid  by  four,  six  or  eight 
tablets,  a  trapezium  by  three,  and  manifold 
instructive  remarks  can  be  made  and  experi- 
ences gathered  in  the  construction  of  these 
figures.  But  above  all,  it  is  the  rhombus 
and  hexagon,  with  which  the  pupil  is  to  be 
made  acquainted  here.  The  child  unites  two 
triangles  by  joining  side  to  side,  and  thus 
produces  a  rhombus. 

The  child  compares  the  sides — are  they 
alike  ?  What  is  their  direction  ?  Are  they 
parallel  ?  Two  and  two  have  the  same  di- 
rection, and  are  therefore  parallel. 

The  child  now  examines  thfe  angles  and 
finds  that  two  and  two  are  of  equal  size. 
They  are  not  right  angles.  Triangles,  smaller 
than  right  angles,  he  knows,  are  called  acute 
angles,  and  he  hears  now  that  the  larger 
ones  are  called  obtuse  angles.  The  teacher 
may  remark  that  the  latter  are  twice  the  size 
of  the  former  ones.  By  these  remarks  the 
pupil  will  gradually  receive  a  correct  idea  of 
the  rhombus  and  of  the  qualities  by  which  it 
is  distinguished  from  the  quadrangle,  right 
angle,  trapezium  and  rhomboid. 
6 


In  the  same  manner,  the  hexagon  gives 
occasion  for  interesting  and  instructive  ques- 
tions and  answers.  How  many  sides  has  it  ? 
How  many  are  parallel  ?  How  many  angles 
does  it  contain  ?  What  kind  of  angles  are 
they  ?  How  large  are  they  as  compared  with 
the  angles  of  the  equal  sided  triangle  ?  Twice 
as  large. 

The  power  of  observation  and  the  reason- 
ing faculties  are  constantly  developed  by  such 
conversation,  and  the  results  of  such  exer- 
cises are  of  more  importance  than  all  the 
knowledge  that  rftay  be  acquired  in  the  mean- 
time. 

The  greater  part  of  this  occupation,  how- 
ever, is  not  within  the  Kinder- Garten  proper, 
but  belongs  to  the  realm  of  the  Primary 
School  Department.  If  they  are  introduced 
in  the  former,  they  are  intended  only  to  swell 
the  sum  of  general  experience  in  regard  to 
the  qualities  of  things,  whereas  in  the  latter, 
they  serve  as  a  foundation  for  real  knowledge 
in  the  department  of  mathematics. 

D.    THE  OBTUSE-ANGLED  TRIANGLE  WITH 
TWO  SIDES  ALIKE. 

(plates  xxvr.  and  xxvil) 

The  child  receives  a  box  with  sixty-four 
obtuse-angled  tablets.  It  examines  one  of 
them  and  compares  it  with  the  right-angled 
triangle,  with  two  sides  alike.  It  has  two 
sides  alike,  has  also  two  acute  angles,  but  the 
third  angle  is  larger  than  the  right  angle  ;  it 
is  an  obtuse  angle,  and  the  tablet  is,  there- 
fore, an  obtuse-angled  triangle  with  two  sides 
alike. 

The  pupil  then  unites  two  and  two  tablets 
by  joining  their  sides,  corners,  sides  and 
corners,  and  vice  versa,  as  shown  in  Figs.  1-8, 
on  Plate  XXVI. 

The  next  preliminary  exercise,  is  the  com- 
bination, by  fours,  of  elementary  forms  thus 
produced.  Peculiarly  beautiful,  mosaic-like 
forms  of  beauty  result  from  this  process. 
The  Figs.  9-15  afford  examples  which  were 
produced  by  combination  of  two  opposites, 
a  and  b,  or  by  mediative  forms  c  and  d.     Ir 


GUIDE   TO    KINDER  GARTNERS. 


Figs'.  16-32  we  have  finally  some  few  sam- 
ples of  forms  of  life. 

The  forms  of  knowledge  which  may  be 
produced,  afford  opportunity  to  repeat  what 
has  been  taught  and  learned  previously  about 
proportion  of  form  and  size.  In  the  Primary 
School  the  geometrical  proportions  are  further 
introduced,  by  which  rqeans  the  knowledge 
of  the  pupils,  in  regard  to  angles,  as  to  the 
position  they  occupy  in  the  triangle,  can  be 
successfully  developed  by  practical  observa- 
tion, without  the  necessity  of  ever  dealing  in 
mere  abstractions. 

E.    THE  RlGHT-ANGLEt)  TRIANGLE  WITH 
NO  EQUAL  SIDES. 

(plates  xxviii.  and  XXIX.) 

The  little  box  with  fifty-six  tablets  of  the 
above  description,  each  of  which  is  half  the 
size  of  the  obtuse-angled  triangle,  enables  the 
child  to  represent  a  goodly  number  of  forms 
of  life,  as  shown  on  Plate  XXIX. 

In  producing  them,  sufiicient  opportunities 
will  present  themselves,  to  let  the  child  find  out 
the  qualities  of  the  new  occupation  material. 

A  comparison  with  the  right  angled  triangle 
with  two  equal  sides  will  facilitate  the  matter 
greatly. 

On  the  whole,  however,  the  process  of  de- 
velopment may  be  pursued,  as  repeatedly  in* 
dicated  on  previous  occasions. 


The  variety  of  the  forms  of  beauty  to  be  laid 
with  these  tablets,  is  especially  founded  on 
their  combination  in  twos.  Plate  XXVIII , 
Figs.  1-6,  shows  the  forms  produced  by  join- 
ing equal  sides. 

In  similar  manner,  the  child  has  to  find  ou. 
the  forms  which  will  be  the  result  of  joining 
unlike  sides,  like  corners,  unlike  corners,  and 
finally,  corners  and  sides. 

By  a  fourfold  combination  of  such  element 
ary  forms  the  child  receives  the  material, 
(Figs.  7-18,)  to  produce  a  large  number  of 
forms  of  beauty  similar  to  those  given  under 
19-22. 

For  the  purpose,  also,  of  presenting  to  the 
child's  observation,  in  a  new  shape,  propor- 
tions of  form  and  size,  in  the  production  of 
forms  of  knowledge,  these  tablets  are  very 
serviceable. 

Like  the  previous  tablets,  these  also,  and  a 
following  set  of  similar  tablets,  are  used  in 
the  Primary  Department  for  enlivening  the 
instruction  in  Geometry.  It  is  believed  that 
nothing  has  ever  been  invented  to  so  facilitate, 
and  render  interesting  to  teacher  and  pupil, 
the  instruction  in  this  so  important  branch  of 
education  as  the  tablets  forming  the  Seventh 
Gift  of  Froebel's  Occupation  Material,  the  use 
of  which  is  commenced  with  the  cl.ildren  when 
they  have  entered  the  second  year  of  then 
Kinder- Garten  discipline. 


THE   EIGHTH    GIFT 


STAFFS  FOR  LAYING  OF  FIGURES. 


(plates  XXX.   TO   XXX in.) 


As  the  tablets  of  the  Seventh  Gift  are 
nothing  but  an  embodiment  of  the  planes  sur- 
rounding or  limiting  the  cube^  "and  as  these 
planes,  limits  of  the  cube,  are  nothing  but 
the  representations  of  the  extension  in  length, 
breadth,  and  height,  already  contained  in  the 
sphere  and  ball,  so  also  the  staffs  are  derived 
from  the  cube,  forming  as  they  do,  and  here 
bodily  representing  its  edges.  But  they  are 
also  contained  in  the  tablets,  because  the 
plane  is  thought  of,  as  consisting  of  a  con- 
tinued or  repeated  line,  and  this  may  be 
illustrated  by  placing  a  sufficient  number  of 
one  inch  long  staffs  side  by  side,  and  close 
together,  until  a  square  is  formed 

The  staffs  lead  us  another  step  farther, 
from  the  material,  bodily,  toward  the  realm 
of  abstractions. 

By  means  of  the  tablets,  we  were  enabled 
to  produce  flat  images  of  bodies  ;  the  slats, 
which,  as  previously  mentioned,  form  a  tran 
sition  from  plane  to  line,  gave,  it  is  true,  the 
oudines  of  forms,  but  these  outlines  still  re- 
tained a  certain  degree  of  the  plane  about 
them  ;  in  the  staffs,  however,  we  obtain  the 
material  to  draw  the  outlines  of  objects,  by 
bodily  lines,  as  perfectly  as  it  can  possibly 
be  done. 

The  laying  of  staffs  is  a  favorite  occupa- 
tion with  all  children.  Their  fantasy  sees  in 
them  the  most  different  objects, — stick,  yard 
measure,  candle ;  in  short,  they  are  to  them 
representatives  of  every  thing  straight. 

Our  staffs  are  of  the  thickness  of  a  line 
(one  twelfth  of  an  inch),  and  are  cut  in  vari- 


ous lengths.  The  child,  holding  the  staff  in 
hand,  is  asked  :  What  do  you  hold  in  your 
hand.''  How  do  you  hold  it?  Perpendicu 
larly.  Can  you  hold  it  in  any  other  way? 
Yes !  I  can  hold  it  horizontally.  Still  in 
another  way?  Slanting  from  left  above,  to 
right  below,  or  from  right  above  to  left 
below. 

Lay  your  staff  upon  the  table.  How  does 
it  lie  ?  In  what  other  direction  can  you  place 
it?     (Plate  XXX.  A.) 

The  child  receives  a  second  staff.  How 
many  staffs  have  you  now  ?  Now  try  to  form 
something.  The  child  lays  a  standing  cross. 
(Fig.  4.)  You  certainly  can  lay  many  other 
and  more  beautiful  things ;  but  let  us  see 
what  else  we  may  produce  of  this  cross,  by 
moving  the  horizontal  staff,  by  half  its  length, 
(Fig.  B.  4  to  14  )  Starting  from  a  lying  cross, 
(C  15 — 23)  or  from  a  pair  of  open  tongs, 
(where  two  acute  and  two  obtuse  angles  are 
formed  by  the  crossing  staffs,)  and  proceeding 
similarly  as  with  B,  we  will  produce  all  posi- 
tions which  two  staffs  can  occupy,  relative  to 
one  another,  except  the  parallel,  and  this  will 
give  ample  opportunity  to  refresh,  and  more 
deeply  impress  upon  the  pupil's  mind,  all  that 
has  been  introduced  so  far,  concerning  per 
pendicular,  horizontal,  and  oblique  lines,  and 
of  right,  acute  and  obtuse  angles.  With  two 
staffs,  we  can  also  form  little  figures,  which 
show  some  slight  resemblance  with  things 
around  us.  By  them  we  enliven  the  power  of 
recollection  and  imagination  of  the  child,  ex 
ercise  his  ability  of  comparison,  increase  his 


40 


GUIDE    TO    KINDER-GARTNERS. 


treasure  of  ideas,  and' develop,  in  all  these 

Fig.  56 

A  Steeple. 

his  power  of  perception  and  conception — the 

Fig.  57- 

A  Funnel. 

most  indispensable  requisites  for  disciplining 

Fig.  58- 

A  Beer  Bottle. 

the  mind. 

Fig-  59- 

A  Bath  Tub. 

Our  plates  give  representations  of  the  fol- 

Fig. 60. 

A  (broken)  Plate. 

lowing  objects : 

Fig.  61. 

A  Roof. 

Fig.  62. 

A  Hat. 

WITH   TWO  STAFFS. 

Fig.  63. 

A  Chair. 

Fig.  24.  A  Playing  Table. 

Fig.  64. 

A  Lamp  Shade, 

Fig.  25.  A  Weather-vane. 

Fig.  65. 

A  Wine  glass. 

Fig.  26.  A  Pickax. 

Fig.  66. 

A  Grate. 

Fig.  27.  An  Angle  measure.     (Carpenter's 

square.) 

WITH   SIX   STAFFS. 

Fig.  28.  A  Candle  stick. 

Fig-  67 

A  Large  Frame. 

Fig.  29.  Two  Candles. 

Fig.  68. 

A  Flag. 

Fig.  30.  Rails. 

Fig.  69. 

A  Barn. 

Fig.  31.   Roof. 

Fig.  70- 

A  Boat. 

Fig.  71- 

A  Reel. 

WITH   THREE  STAFFS. 

Fig.  72. 

A  Small  Tree. 

Fig.  32    A  Kitchen  Table. 

Fig  73. 

A  Round  Table. 

Fig.  33.  A  Garden  Rake. 

Fig.  34.   A  Flail. 

WITH  SEVEN  STAFFS, 

Fig.  35.  An  Umbrella. 

Fig.  74. 

A  Window. 

Fig.  36.  A  Hay  Fork. 

Fig.  75- 

A  Stretcher. 

Fig.  37.  A  Small  Flag. 

Fig.  76. 

A  Dwelling-house. 

Fig.  38.  A  Steamer. 

Fig-  77- 

Steeple  with  Lightning  rod. 

Fig.  39.  A  Whorl. 

Fig.  78. 

A  Balance.                            » 

Fig.  40.  A  Star. 

Fig.  79- 

Piano  forte. 

Fig.  80. 

A  Bridge  with  Three  Spans. 

WITH   FOUR   STAFFS. 

Fig.  81. 

An  Inn  Sign, 

Fig.  41.  A  Small  Looking-glass. 

Fig.  82. 

Crucifix  and  Two  Candles. 

Fig.  42.  A  Wooden  Chair. 

Fig.  83. 

Tombstone  and  Cross. 

Fig.  43.  A  Wash-bench. 

Fig.  84. 

Rail  Fence. 

Fig.  44.  Kitchen  Table  with  Candle. 

Fig.  85. 

Garret  Window. 

Fig.  45.  A  Crib. 

Fig.  86. 

Flower  Spade. 

Fig.  46.  A  Kennel. 

Fig.  87. 

A  Star  Flower. 

Fig.  47.  Sugar-loaf. 

Fig.  48.  Flowerpot. 

WITH   EIGHT   STAFFS. 

Fig.  49.   Signal-post. 

Fig.  88. 

Book-shelves. 

Fig.  50.  Flower-stand, 

Fig.  89. 

Church,  with  Steeple. 

Fig.  51.  Crucifix. 

Fig.  90. 

Tombstone  and  Cross. 

Fig   52.  A  Grate. 

Fig-  91- 

Gas  Lantern. 

Fig.  92. 

Windmill. 

WITH   FIVE  STAFFS. 

Fig.  93- 

A  Tower. 

Fig.  53.  Signal  Flag  of  R.  R.  Guard. 

Fig.  94. 

An  Umbrella. 

Fig.  54.  Chest  of  Drawers. 

Fig-  95- 

A  Carrot. 

Fig.  55.  A  Cottage. 

Fig.  96. 

A  Flovver-poL 

GUIDE  TO    KINDER-GARTNERS. 


41 


Fig. 

97- 

A  large  Wash  tub. 

Fig. 

98. 

A  large  Rail  Fence. 

Fig. 

99. 

A  large  Kitchen  Table. 

Fig 

100. 

A  Shoe. 

Fig. 

lOI. 

A  Butterfly. 

Fig. 

102. 

A  Kite. 

WITH    NINE   STAFFS. 
Fig.  103.   Church  with  Two  Steeples. 
Fig.  104.  Dwelling-house. 
Fig.  105.  Coffee-mill. 
Fig.  106.  Kitchen  Lamp. 
Fig.  io7.  Sail-boat. 
Fig.  loS.  Bilance. 

WITH   TEN   STAFFS. 

Fig.  109.  A  Tower. 

Fig.  no.  A  Drum. 

Fig.  III.  Grave-yard  Wall. 

Fig.  1X2.  A  Hall. 

Fig.  113.  A  Flower  pot. 

Fig.  114  A  Street  Lamp. 

Fig.  115.  A  Satchel. 

Fig.  116.  A  Double  Frame. 

Fig.  117.  A  Bedstead. 

Fig.  118.  A  row  of  Barns. 

Fig.  119.  A  Flag. 

WITH   ELEVEN   STAFFS. 
Fig.  120-  A  Kitchen  Lamp. 
Fig.  121.  A  Pigeon-house. 
Fig,  122.   A  Farm-house. 
Fig.  123.  A  Sail-boat. 
Fig.  124.  A  Student's  Lamp. 

WITH  TWELVE  STAFFS. 
Fig.  125.  A  Church.     • 
Fig.  126.   A  Window. 
Fig.  127.  Chair  and  Table. 
Fig.  128.  A  Well  with  Sweep. 

These  exercises  are  to  be  continued  with  a 
larger  number  of  staffs.  The  hints  given 
above,  will  enable  the  teacher  to  conduct  the 
laying  of  staffs  in  a  manner  interesting,  as  well 
as  useful,  for  her  pupils. 

It  is  advisable  to  guide  the  activity  oi  the 


child  occasionally  in  another  direction.  The 
pupils  may  all  be  called  upon  to  lay  tables, 
which  can  be  produced  from  two  to  ten  staffs,  or 
houses  which  can  be  laid  with  eighteen  staffs. 

Another  change  in  this  occupation  can  be 
introduced  by  employing  two,  four,  or  eight 
times,  divided  staffs.  It  is  obvious  that,  in 
this  manner,  the  figures  may  often  assume  a 
greater  similarity  and  better  proportions  than 
is  possible  if  only  staffs  of  the  same  length  are 
employed. 

If  a  staff  is  not  entirely  broken  through, 
but  only  bent  with  a  break  on  one  side,  an 
angle  is  produced.  If  a  staff  forms  several 
such  angles,  it  can  be  used  to  represent  a 
curved  or  rounded  line,  and  by  so  doing  a  new 
feature  is  introduced  to  the  class. 

Staffs  are  also  employed  for  representing 
forms  of  beauty.  The  previous,  or  simulta- 
neous occupation  with  the  building  blocks, 
and  tablets,  will  assist  the  child  in  producing 
the  same  in  great  variety.  Figures  121 — 124 
on  Plate  XXXIII.  belong  to  this  class  of  repre- 
sentations. 

Combination  of  the  occupation  material  of 
several,  or  all  children  taking  part  in  the  ex- 
ercises, will  lead  to  the  production  of  larger 
forms  of  life,  or  beauty,  which  in  the  Primary 
Department,  can  even  be  extended  to  repre- 
senting whole  landscapes,  in  which  the  mate- 
rial is  augmented  by  the  introduction  of  saw- 
dust to  represent  foliage,  grass,  land,  moss, 
etc.  Plate  XXXIII.  gives,  under  Fig.  120,  a 
specimen  of  such  a  production — on  a  very  re- 
duced scale. 

By  means  of  combination,  the  children 
often  produce  forms  which  afford  them  great 
pleasure,  and  repay  them  for  the  careful  per- 
severance and  skill  employed.  They  often 
express  the  wish  that  they  might  be  able  to 
show  the  production  to  father,  or  mother,  or 
sister,  or  friend.  But  this  they  cannot  do,  as 
the  staffs  will  separate  when  taken  up. 

We  should  assist  the  little  ones  in  carrying, 
out  their  desire  of  giving  pleasure  to  others 
by  showing  to,  or  presenting  them  with  th< 
result  of  their  own  industry,  in  portable  form 


42 


GUIDE    TO    KINDER-GARTNERS. 


By  wetting  the  ends  of  the  staffs  with  mucil- 
age, or  binding  them  together  with  needle 
and  thread,  or  placing  them  on  substantial 
paper,  we  can  grant  their  desire,  and  make 
them  happy,  and  be  sure  of  their  thanks  for 
our  efforts. 

We  employ  the  same  means  of  rendering 
permanent  the  production  of  staff-laying  in 
our  instruction  in  reading,  where  letters  are 
fastened  to  paper  by  mucilage,  thus  impress- 
ing upon  the  child's  mind  more  lastingly,  the 
visible  signs  of  the  s  xmds  he  has  learned. 

But  we  have  still  another  means  of  render- 
ing these  Representations  permanent,  and  it  is 
by  drawings  which,  on  its  own  account,  is  to 
be  practiced  in  the  most  elementary  manner. 
We  begin  the  drawing,  as  will  hereafter  be 
shown,  as  a  special  branch  of  occupation,  as 
soon  as  the  child  has  reached  its  third  or 
fourth  year. 

The  child  is  provided  with  a  slate,  upon 
whose  surface,  a  net  work  of  horizontal  and 
perpendicular  lines  is  drawn.  Instead  of  lay- 
ing the  staff  upon  the  table,  the  child  places 
it  upon  the  slate.  Taking  the  staff  from  its 
place,  he  draws  with  the  slate  pencil,  in  its 
stead,  a  line  as  long  as  the  staff,  in  the  same 
direction.  He  draws  the  perpendicular  staff. 
The  horizontal,  slantingly  laid  staff,  is  drawn 
in  all  its  variations  in  like  manner,  perpendic- 
ular, and  horizontal ;  perpendicular  and  ob- 
lique, or  horizontal  and  oblique  staffs  are 
brought  in  contact  with  one  another,  and 
these  connections  reproduced  by  drawing. 

The  method  of  laying  staffs  is  in  general 
the  same,  applied  for  drawing,  the  latter,  how- 
ever, progresses  less  rapidly.  It  is  advisable 
to  combine  staffs  in  regular  figures,  triangles 
and  squares,  and  to  find  out  in  a  small  num- 
ber of  such  figures  all  possible  combinations 
according  to  the  law  of  opposites.  Plates 
XXIV.  and  XXV.  will  furnish  material  for  this 
purpose. 

All  these  occupations  depend  on  the  larger 
or  smaller  number  of  staffs  employed  ;  they 
therefore  afford  means  for  increasing  and 
strengthening   the    knowledge   of  the   child. 


The  pupil,  however,  is  much  more  decidedly 
introduced  into  the  elements  of  ciphering, 
when  the  staffs  are  placed  into  his  hands  for 
this  specific  purpose.  We  do  not  hesitate  to 
make  the  assertion  that  there  is  no  material 
better  fitted  to  teach  the  rudiments  in  figures, 
as  also  the  more  advanced  steps  in  arithme 
tic,  than  Froebel's  staffs,  and  that  by  their  in- 
troduction, all  other  material  is  rendered  use- 
less. A  few  packages  of  the  staffs  in  the 
hands  of  the  pupil  is  all  that  is  needed  in  the 
Kinder  Garten  proper,  and  the  following  De- 
partment of  the  Primary. 

The  children  receive  a  package  with  ten 
staffs  each.  Take  one  staff  and  lay  it  per- 
pendicularly on  the  table.  Lay  another  at 
the  side  of  it.  How  many  staffs  are  now  be- 
fore you  ?     Twice  one  makes  two. 

Lay  still  another  staff  upon  the  table. 
How  many  are  there  now  ?  One  and  one 
and  one — two  and  one  are  three. 

Still  another,  etc.,  etc.,  until  all  ten  staffs 
are  placed  in  a  similar  manner  upon  the 
table.  Now  take  away  one  staff.  How  many 
remain?  Ten  less  one  leaves  nine  Take 
away  another  staff  from  these  nine.  How 
many  are  left?      Nine  less  one  leaves  eight. 

Take  another;  this  leaves ?  seven,  etc., 

etc.,  until  all  the  staffs  are  taken  one  by  one 
from  the  table,  and  are  in  the  child's  hand 
again.  Take  two  staffs  and  lay  them  upon 
the  table,  and  place  two  others  at  some  dis- 
tance from  them.  (||  ||)  How  many  are  now 
on  the  table  ?  Two  and  two  are  four.  Lay 
two  more  staffs  beside  these  four  staffs.  How 
many  are  there  now  ?  Four  and  two  are  six. 
Two  more.  How  many  are  there  now.-*  Six 
and  two  are  eight.  And  still  another  two. 
How  many  now  ?     Eight  and  two  are  ten. 

The  child  has  learned  to  add  staffs  by  twos. 
If  we  do  the  opposite,  he  will  also  learn  to 
subtract  by  twos.  In  similar  manner  we  pro- 
ceed with  three,  four,  zxi^five.  After  that,  we 
alternate,  with  addition  and  subtraction.  For 
instance,  we  lay  three  times  two  staffs  upon  the 
table  and  take  away  twice  two,  adding  again 
four   times    two.      Finally    we   give   up    the 


GUIDE    TO   KINDER-GARTNERS. 


43 


equality  of  the  number  and  alternate,  by  ad- 
ding different  numbers.  We  lay  upon  the 
table  2  and  3  staffs=5,  adding  2=7  adding 
3:=rio.  This  affords  opportunity  to  intro- 
duce 6  and  9,  as  a  whole,  more  frequently 
than  was  the  case  in  previous  exercises.  In 
subtraction  we  observe  the  same  method,  and 
introduce  exercises  in  which  subtraction  and 
addition  alternate  with  unequal  numbers. 
Lay  6  staffs  upon  the  table,  take  2  aWay,  add 
4,  take  away  i,  add  3,  and  ask  the  child  how 
many  staffs  are  on  the  table,  after  each  of 
these  operations. 

In  like  manner,  as  the  child  learned  the 
figures  from  one  to  ten,  and  added  and  sub 
tracted  with  them  as  far  as  the  number  of  10 
staffs  admitted,  it  will  now  learn  to  use  the 
Id's  up  to  100.  Packages  of  10  staffs  are 
distributed.  It  treats  each  package  as  it  did 
before  the  single  staff.  One  is  laid  upon  the 
table,  and  the  child  says,  ''Once  ten  ;"  add  a 
second,  "  Twice  ten  ; "  a  third,  "  Three  times 
ten,"  etc.  Subsequently  it  is  told,  that  it  is 
not  c'ustomary  to  say  twice,  or  two  times  ten, 
but  twenty ;  not  three  times  ten,  but  thirty, 
etc.  This  experience  will  take  root  so  much 
the  sooner,  in  his  memory,  and  become 
knowledge,  as  all  this  is  the  result  of  his  own 
activity. 

As  soon  as  the  child  has  acquired  sufficient 
ability  in  adding  and  subtracting  by  tens,  the 
combination  of  units  and  tens  is  introduced. 

The  pupil  receives  two  packages  of  ten 
staffs — places  one  of  them  upon  the  table, 
opens  the  second  and  adds  its  staffs  one  by 
one  to  the  ten  contained  in  the  whole  pack- 
age. He  learns  10  and  1  =  1  r,  10  and  2=12, 
10  and  3  =  13,  until  10  and  10  =  20  staffs. 
Gathering  the  10  loose  staffs,  the  child  re- 
ceives another  package  and  places  it  beside 
the  first  whole  package.  10  and  10  —  20 
staffs.  Then  he  adds  one  of  the  loose  staffs, 
arid  says  20  and  1^21,  20  and  2  =  22,  etc. 
Another  package  of  10  brings  the  number  to 
31,  etc.,  etc.,  up  to  91  staffs.  In  this  manner 
he  lea.'ns  22.  32,  up  to  92,  23  to  93,  and  too. 
and   to  :x\d    and   subtract  within   this  limit. 


To  be  taught  addition  and  subtraction  in 
this  manner,  is  to  acquire  sound  knowledge, 
founded  on  self-activity  and  experience,  and 
is  far  superior  to  any  kind  of  mind  killing 
memorizing  usually  employed  in  this  connec- 
tion. 

If  addition  and  subtraction  are  each  other's 
opposites,  so  addition  and  multiplication  on 
the  one  hand,  and  subtraction  and  division 
on  the  other,  are  oppositionally  equal,  or, 
rather,  multiplication  and  division  are  short- 
ened addition  and  subtraction. 

In  addition,  when  using  equal  numbers  of 
staffs,  the  child  finds  that  by  adding  2  and  2 
and  2  and  2  staffs  it  receives  8  staffs,  and  is 
told  that  this  may  also  be  expressed  by  saying 
4  times  2  staffs  are  8  staffs.  It  will  be  easy 
to  see  how  to  proceed  with  division,  after  the 
hints  given  above. 

It  has  been  previously  mentioned  that  for 
the  representation  of  forms  of  life  and  beauty, 
the  staffs  frequently  need  to  be  broken.  This 
provides  material  for  teaching  fractions,  in  the 
meantime.  The  child  learns  by  observtion 
i  staff,  i,  i,  i,  etc.  The  .proportion  of  the 
part  or  of  several  equal  parts  to  the  whole, 
becomes  clear  to  him,  and  finally  it  learns  to 
add  and  subtract  equal  fractions,  in  element- 
ary form,  in  the  same  rational  manner. 

Let  none  of  our  readers  misunderstand  us 
as  intimating  that  all  this  should  be  accom- 
plished in  the  Kinder  Garten  proper. 

Enough  has  been  accomplished  if  the  child 
in  the  Kinder  Garten,  by  means  of  staffs  and 
other  material  of  occupation,  has  been  en- 
abled to  have  a  clear  understanding  of  figures 
in  general. 

This  will  be  the  basis  for  further  develop- 
ment in  addition,  subtraction,  multiplication 
and  division  in  the  Primary  Department. 

It  now  rerftains  to  add  th'fe  necessary  advice 
in  regard  to  the  introduction  and  representa- 
tion with  staffs  of  the  numerals.  In  order  to 
make  the  children  understand  what  numerals 
are,  use  the  blackboard  and  show  them  that 
if  we  wish  to  m.nrk  down  how  many  staffs, 
blocks,  or  other  things  each  of  the  children 


44 


GUIDE   TO   KINDER-GARTNERS. 


have,  we  might  make  one  line  for  each  staff, 
block,  etc.  Write  then  one  small  perpendicu- 
lar line  on  the  blackboard,  saying  in  writing, 
Charles  has  one  staff;  making  hvo  lines  below 
the  first,  continue  by  saying,  Emma  has  two 
blocks ;  again,  making  three  lines,  Ernest  has 
three  rubber  balls,  and  so  on  until  you  have 
written  ten  lines,  always  giving  the  name  of 
the  child  and  stating  bow  many  objects  it  has. 
Then  write  opposite  each  row  of  lines  to  the 
right,  the  Arabic  figure  expressing  the  number 
of  lines,  and  remark  that  instead  of  using  so 
many  lines,  we  can  also  use  these  figures, 
which  we  call  niimeiah.  Then  represent  with 
the  little  staff  these  Arabic  figures,  some  of 
which  require  the  bending  of  some  of  the 
staffs,  on  account  of  the  curved  lines. 

After  the  children  have  learned  that  the 
figures  which  we  use  for  marking  down  the 
number  of  things  are  called  numerals,  exer- 
cises of  the  following  character  may  be  intro- 
duced : 

How  many  hands  has  each  of  you  ?  Two. 
The  numeral  2  is  written  on  the  board.  How 
many  fingers  on  each  hand  ?  Five.  This  is 
written  also  on  the  board — 5.  How  many 
walls  has  this  room  ?  Four.  Write  this  figure 
also  on  the  board.  How  many  days  in  the 
week  are  the  children  in  the  Kinder-Garten  .-• 
Six  days.    The  6  is  also  written  on  the  board. 

Then  repeat,  and  let  the  children  repeat 
after  you,  as  an  exercise  in  speaking,  and  at 
the  same  time,  for  the  purpose  of  recollecting 
the  numerals  : 

Each  child  has  2  hands,  on  each  hand  are 
5  fingers  ;  this  room  has  4  walls, — always 
emphasizing  the  numerals,  and  pointing  to 
them  when  they  are  named. 

The  children  may  then  count  the  objects  in 
the  room,  or  elsewhere,  and  then  lay,  with 
their  staffs,  the  numerals  expressing  the  num- 
ber they  have  found,  speaking  in  the  mean 
time,  a  sentence  asserting  the  fact  which  they 
have  stated. 

After  having  introduced  the  numerals  in 
this  manner,  the  teacher,  on  some  following 
day,  may  proceed  to  reading  exercises. 


The  second  part  of  this  Guide  contains 
systematically  arranged  material  for  instruc 
tion  in  reading,  according  to  the  phonetic 
method. 

Suffice  it  to  say,  that  it  is  begun  in  the 
same  manner  in  which  numerals  were  intro- 
duced. As  by  means  of  numerals,  I  could 
mark  on  the  blackboard  the  number  of  things, 
so  I  can  also  mark  on  the  board  the  names  of 
things,  their  qualities  and  actions.  In  doing 
this  I  write  words,  and  words  consist  of  let 
ters.  Besides  the  words  expressing  names  of 
things,  their  qualities  and  actions,  which  are 
the  most  important  words  in  every  language, 
there  are  other  words  which  are  used  for 
other  purposes.  Such  words  are,  for  example, 
no,  now,  never.  Should  I  ask  you,  is  any  one 
of  you  asleep,  what  would  you  answer  ?  ''  No, 
sir.  We  are  j|ll  awake."  I  will  write  the  lit 
tie  word  "  no^  on  the  blackboard,  because  it 
is  the  most  important  word  in  your  answer. 
There  it  stands,  "  no'^  And  now  I  will  ask  you : 
"Have  you  ever  been  in  a  Kinder- Garten  ?" 
"Yes,  sir,  we  are  now  in  a  Kinder-Garten 
school."  I  will  write  on  the  board  the  little 
word,  "  no7v."  There  it  stands,  ^'  now  y-"  an(J 
another  question  I  will  now  ask  you  :  "  Should 
we  ever  kill  an  animal  for  the  mere  pleasure 
of  hurting  it?"  "  No,  sir,  w^zrr."  I  will  also 
write  flie  word  '■'■never,'"  on  the  board.  There 
it  is,  ^^ never."  I  will  now  pronounce  these 
three  words  for  you,  and  each  of  you  will 
repeat  them  in  the  same  manner  in  which  I 
do.  N o!  N ow!  N ever!  Chil- 
dren, in  repeating,  always  dwell  on  the  n 
sound  longer  than  on  any  other  part  of  the 
word.  They  are  then  led  to  observe  the 
similarity  of  sound  in  pronouncing  the  three 
words,  then  to  observe  the  similarity  of  the 
first  letter  in  all  of  them,  and  finally  the  dis- 
similarity of  the  remaining  part  of  the  words 
in  sound,  and  its  representations — the  letters. 

I  will  now  take  away  these  words  from 
the  blackboard,  and  write  something  else  upon 
it.  I  again  write  the  "«/'  and  the  children 
will  soon  recognize  it  as  the  letter  previously 
shown. 


GUIDE    TO    KINDER-GARTNERS. 


45 


For  the  continuation  of  instruction  in  read- 
ing, we  refer  the  reader  to  tlie  second  part  of 
the  ■•  Guide,"  where  all  necessary  information 
on  this  important  branch  of  instruction  will 
be  iound. 

As  the  occupation  with  laying  staffs,  is  one 


of  the  earliest  in  the  Kinder  Garten,  and  is  em- 
ployed in  teaching  numerals,  and  reading  and 
writing,  and  drawing  also,  it  is  evident  how 
important  a  material  of  occupation  was  sup- 
plied by  Froebel,  in  introducing  the  staffs  as 
one  of  his  Kinder-Garten  Gifts. 


THE    NINTH    GIFT. 


WHOLE   AND   HALF   RINGS    FOR   LAYING    FIGURES. 


(PLATE   XXX IV.) 


Immediately  connected  with  the  staffs,  or 
straight  lines,  Froebel  gives  the  representa- 
tives of  the  rounded,  curved  lines,  in  a  box 
containing  twenty-four  whole  and  forty-eight 
half  circles  of  two  different  sizes  made  of 
wire.  We  have  heretofore  introduced  the 
curved  line  by  bending  the  staff;  this,  how- 
ever, was  a  rather  imperfect  representation. 
The  rings  now  introduced  supply  the  means 
ot  representing  a  curved  line  perfectly,  be- 
sides enabling  us  by  their  different  sizes  to 
show  '■  the  one  within  another"  more  plainly 
than  it  could  be  done  with  the  staffs,  as  the 
above,  upon,  below,  aside  of  each  other,  etc.,  could 
well  be  represented,  but  not  the  *'  within  "  in 
a  perfectly  clear  manner. 

This  Gift  is  introduced  in  the  same  way  as 
all  other  previous  Gifts  were  introduced,  and 
the  rules  by  which  this  occupation  is  carried 
on  must  be  clear  to  every  one  who  has  fol 
lowed  us  in  our  •'  Guide  "  to  this  point. 

The  child  receives  one  whole  ring  and  two 
half  rings  of  the  larger  size.  Looking  at  the 
whole  ring  the  children  observe  that  there  is 
neither  beginning  nor  end  in  the  ring — that  it 
represents  the  circle,  in  which  there  is  neither 
beginning  nor  end.  With  the  half  ring,  they 
have  two  ends  ;  half  rings,  like  half  circles 
and  all  other  parts  of  the  circle  or  curved 
lines,  have  two  ends.     Two  of  the  half  rings 


form  one  whole  ring  or  circle,  and  the  chil- 
dren are  asked  to  show  this  by  experiment, 
(Fig.  I,  Plate  XXXIV).  Various  observations 
can  be  made  by  the  children,  accompanied  by 
remarks  on  the  part  of  the  teacher.  When- 
ever the  child  combined  two  cubes,  two  tablets, 
staffs  or  slats  with  one  another,  in  all  cases 
where  corners  and  angles  and  ends^  were  con- 
cerned in  this  combination,  corners  and  angles 
were  again  produced.  The  two  half  rings  or 
half  circles,  however,  do  not  form  any  angles. 
Neither  could  closed  space  be  pi  educed  by 
two  bodies,  planes,  nor  lines ! — the  two  half 
circles,  however,  close  tightly  up  to  each 
other,  so  that  no  opening  remains. 

The  child  now  places  the  two  half  circles 
in  opposite  directions,  (Fig.  i.)  Before  the 
ends  touched  one  another,  now  the  middle  of 
the  half  circles  ;  previously  a  closed  space 
was  formed,  now  both  half  circles  are  open, 
and  where  they  touch  one  another,  angles 
appear 

Mediation  is  formed  in  Fig.  3,  where  both 
half  circles  touch  each  other  at  one  end  and 
remain  open,  or,  as  indicated  by  the  dotted 
line,  join  at  end  and  middle,  thereby  enclosing 
a  small  plane  and  forming  angles  in  the  mean- 
time. 

Two  more  half  circles  are  presented.  The 
child  forms  Fig.  4,  and  develops  by  moving 


46 


GUIDE   TO    KINDER-GARTNERS. 


the  half  circles  in  the  direction  from  without, 
to  within  Fig    5,  6,  7,  and  8. 

The  number  of  circles  is  increased.  Fig- 
9,  10,  and  II  show  some  forms  built  of  8  half 
circles. 

All  these  forms  are,  owing  to  the  nature  of 
the  circular  line,  forms  of  beauty,  or  beauti- 
ful forms  of  life,  and,  therefore,  the  occupa- 
tion with  these  rings,  is  of  such  importance. 
The  child  produces  forms  of  beauty  with 
other  material,  it  is  true,  but  the  curved  line 
suggests  to  him  in  a  higher  degree  than  any- 
thing else,  ideas  of  the  beautiful,  and  the 
simplest  combinations  of  a  small  number  of 
half  and  whole  circles,  also  bear  in  themselves 
the  stamps  of  beauty. 

If  the  fact  cannot  be  refuted,  that  merely 
looking  at  the  beautiful,  favorably  impresses 
the  mind  of  the  grown  person,  in  regard  to 
direction  of  its  development,  enabling  him  to 
more  fully  appreciate  the  good,  and  true,  and 
noble,  and  sublime,  this  influence,  upon  the 
tender  and  pliable  soul  of  the  child,  must 
needs  be  greater,  and  more  lasting.  Without 
believing  in  the  doctrine  of  two  inimical 
natures  in  man,  said  to  be  in  constant  con- 
flict with  each  other,  we  do  believe  that  the 


talents  and  disposition  in  human  nature  are 
subject  to  the  possibility  of  being  developed 
in  two  opposite  directions.  It  is  this  possi 
bility,  which  conditions  the  necessity  of  edu- 
cation, the  necessity  of  employing  every 
means  to  give  the  dormant  inclinations  and 
tastes  in  the  child,  a  direction  toward  the 
true,  and  good,  and  beautiful, — in  one  word, 
toward  the  ideal.  Among  these  means,  stands 
pre-eminently  a  rational  and  timely  develop- 
ment of  the  sense  of  beauty,  upon  which 
Froebel  lays  so  much  stress. 

Showing  the  young  child  objects  of  art  which 
are  far  beyond  the  sphere  of  its  appreciation, 
however,  will  assist  this  development,  much 
less  than  to  carefully  guard  that  its  surround- 
ings contain,  and  show  the  fundamental  req- 
uisites of  beauty,  viz. :  order,  cleanHness,  sim- 
plicity, and  harmony  of  form,  and  giving  as- 
sistance to  the  child  in  the  active  representa- 
tion to  the  beautiful  in  a  manner  adapted  to 
the  state  of  development  in  the  child  himself. 

Like  forms  laid  with  staffs,  those  repre- 
sented with  rings  and  half  rings  also,  are 
imitated  by  the  children  by  drawing  them  on 
slate  or  paper. 


THE    TENTH    GIFT. 


THE   MATERIAL   FOR   DRAWING. 

(plates  XXXV.   TO   XLVI.) 


One  of  the  earliest  occupations  of  the  child 
should  be  methodical  drawing.  Froebel  s 
opinion  and  conviction  on  this  subject,  de- 
viates from  those  of  other  educators,  as  much 
9.S  in  other  respects.  Froebel,  however,  does 
not  advocate  drawing,  as  it  is  usually  prac- 
ticed, which  on  the  whole,  is  nothing  else  but 
a  more  or  less  thoughtless  mechanical  copy- 


ing. The  method  advanced  by  Froebel,  is  in- 
vented by  him,  and  perfected  in  accordance 
with  his  general  educational  principles. 

The  pedagogical  effect  of  the  customary 
method  of  instruction  in  drawing,  rests  in 
many  cases  simply  in  the  amount  of  trouble 
caused  the  pupil  in  surmounting  technical 
difficulties.     Just  for  that  reason  it  should  be 


GUIDE    TO    KINDER-GARTNERS. 


47 


abandoned  entirely  for  the  youngest  pupils, 
for  the  difficulties  in  many  cases  are  too  great 
for  the  child  to  cope  with.  It  is  a  work  of 
Sisyphus,  labor  without  result,  naturally  tend- 
ing to  extirpate  the  pleasure  of  the  child  in  its 
occupation,  and  the  unavoidable  consequence 
is  that  the  majority  of  people  will  never  reach 
the  point  where  they  can  enjoy  the  fruits  of 
their  endeavors. 

If  we  acknowledge  that  Froebel's  educa- 
tional principles  are  correct,  namely,  that  all 
manifestations  of  the  child's  life  are  manifes- 
tations of  an  innate  instinctive  desire  for 
development,  and  therefore  should  be  fos. 
tered  and  developed  by  a  rational  education, 
in  accordance  with  the  laws  of  nature.  Draw- 
ing should  be  commenced  with  the  third  year; 
nay,  its  preparatory  principles  should  be  intro- 
duced at  a  still  earlier  period. 

With  all  the  gifts,  hitherto  introduced,  the 
children  were  able  to  study  and  represent 
forms  and  figures.  Thus  they  have  been 
occupied,  as  it  were,  in  drawing  tvith  bodies. 
This  developed  their  fantasy,  and  taste,  giving 
them  in  the  meantime  correct  ideas  of  the 
solid,  plane,  and  the  embodied  line. 

A  desire  soon  awakes  in  the  child,  to  rep- 
resent by  drawing  these  lines  and  planes, 
these  forms  and  objects.  He  is  desirous  of 
representation  when  he  requests  the  mother 
to  tell  him  a  story,  explain  a  picture.  He  is 
occupied  in  representation  when  breathing 
against  the  window-pane,  and  scrawling  on  it 
with  its  finger,  or  when  trying  to  make  figures 
in  the  sand  with  a  little  stick.  Each  child  is 
delighted  to  show  what  it  can  make,  and 
should  be  assisted  in  every  way  to  regulate 
diis  desire. 

Drawing  not  only  develops  the  power  of 
representing  things  the  mind  has  perceived, 
but  affords  the  best  means  for  testing  how  far 
they  have  been  perceived  correctly. 

It  was  Froebel's  task  to  invent  a  method 
adapted  to  the  tender  age  of  the  child,  and 
its  slight  dexterity  of  hand,  and  in  the  mean- 
time to  satisfy  the  claim  of  all  his  occupa- 
tions, /'.  e.,  that  the  child  should  not  simply 


imitate,  but  proceed,  self-actingly,  to  perform 
work  which  enables  him  to  reflect,  reason, 
and  finally  to  invent  himself. 

Both  claims  have  been  most  ingeniously 
satisfied  by  Froebel.  He  gives  the  three 
years'  old  child  a  slate,  one  side  of  which  is 
covered  by  a  net-work  of  engraved  lines  (one- 
fourth  of  an  inch  apart),  and  he  gives  him  in 
addition,  thereto,  the  law  of  opposites  and 
their  mediation  as  a  rule  for  h"s  activity. 

The  lines  of  the  net  work  guide  the  child  in 
moving  the  pencil,  they  assist  it  in  measuring 
and  comparing  situation  and  position,  size 
and  relative  center,  and  sides  of  objects. 
This  facilitates  the  work  greatly,  and  in  con- 
sequence of  this  important  assistance  the 
childs'  desire  for  work  is  materially  increased ; 
whereas,  obstacles  in  the  earliest  attempts  at 
all  kinds  of  work  must  necessarily  discourage 
the  beginner. 

Drawing  on  the  slate,  with  slate  pencil  is 
followed  by  drawing  on  paper  with  lead 
pencil.  The  paper  of  the  drawing  books  is 
ruled  like  the  slates.  It  is  advisable  to  begin 
and  continue  the  exercises  in  drawing  on 
paper,  in  like  manner  as  those  on  the  slate 
were  begun  and  continued,  with  this  differ- 
ence only,  that  owing  to  the  progress  made 
and  skill  obtained  by  the  child,  less  repeti- 
tions may  be  needed  to  bring  the  pupil  to 
perfection  here,  as  was  necessary  in  the  use 
of  the  slate. 

It  has  been  repeatedly  suggested,  that 
whenever  a  new  material  for  occupation  is 
introduced,  the  teacher  should  comment  upon, 
or  enter  into  conversation  with  the  children, 
about  the  same  ;  the  difference  between  draw- 
ing on  the  slate  and  on  paper,  and  the  mate- 
rial used  for  both  may  give  rise  to  many 
remarks  and  instructive  conversation. 

It  may  be  mentioned  that  the  slate  is  first 
used,  because  the  children  can  easily  correct 
mistakes  by  wiping  out  what  they  have  made, 
and  that  they  should  be  much  more  careful  in 
drawing  on  paper,  as  their  productions  can 
not  appear  perfectly  clean  and  neat  if  it 
should  be  necessary  to  use  the  rubber  often. 


48 


GUIDE    TO    KINDER- GARTNERS. 


Slate  and  slate  pencil  are  of  the  same  mate- 
rial ;  paper  and  lead  pencil  are  two  very  differ- 
ent things.  On  the  slate  the  lines  and  figures 
drawn,  appear  white  on  darker  ground.  On 
the  paper,  lines  and  figures  appear  black  on 
white  ground. 

More  advanced  pupils  use  colored  lead 
pencils  instead  of  the  common  black  lead 
pencils.  This  adds  greatly  to  the  appear- 
ance of  the  figures,  and  also  enables  the  child 
to  combine  colors  tastefully  and  fittingly.  For 
the  development  of  their  sense  of  color,  and 
of  taste,  these  colored  mosaic  like  figures  are 
excellent  practice. 

Drawing,  as  such,  requires  observation,  at- 
tention, conception  of  the  whole  and  its  parts, 
the  recollection  of  all,  power  of  invention  and 
combination  of  thought.  Thus,  by  it,  mind 
and  fantasy  are  enriched  with  clear  ideas  and 
true  and  beautiful  pictures.  For  a  free  and 
active  development  of  the  senses,  especially 
eye  and  feeling,  drawing  can  be  made  of  in- 
calculable benefit  to  the  child,  when  its  natu- 
ral instinct  for  it  is  correctly  guided  at  its 
very  awakening. 

Our  Plates  XXXV.  to  XLVI.  show  the  sys- 
tematic course  pursued  in  the  drawing  depart- 
ment of  the  Kinder-Garten.  The  child  is  first 
occupied  by 

THE   PERPENDICULAR   LINE. 
(plates  xxxv.  to  xxxviii.) 

The  teacher  draws  on  the  slate  a  perpen- 
dicular line  of  a  single  length  (^  of  an  inch), 
saying  while  so  doing.  I  draw  a  line  of  a  single 
length  downward.  She  then  (leaving  the  line 
on  the  slate,  or  wiping  it  out)  requires  the 
child  to  do  the  same.  She  should  show  that 
the  line  she  made  commenced  exactly  at  the 
crossing  point  of  two  lines  of  the  net- work, 
and  also  ended  at  such  a  point. 

Care  should  be  exercised  that  the  child 
hold  the  pencil  properly,  not  press  too  much 
or  too  little  on  the  slate,  that  the  lines  drawn 
be  as  equally  heavy  as  possible,  and  that  each 
single  line  be  produced  by  one  single  stroke 
of  the  pencil.     The  teacher  should  occasion- 


ally ask  :  What  are  you  doing  ?  or,  what  have 
you  done.-*  and  the  child  should  always  an- 
swer in  a  complete  sentence,  showing  that  it 
works  understandingly.  Soon  the  lines  may 
be  drawn  upwards  also,  and  then  they  may 
be  made  alternately  up  and  down  over  the 
entire  slate,  until  the  child  has  acquired  a  cer- 
tain degree  of  ability  in  handling  the  pencil. 

The  child  is  then  required  to  draw  a  per- 
pendicular line  of  two  lengths,  and  advances 
slowly  to  lines  of  three,  four  and  five  lengths, 
(Plate  XXXV.,  Figs.  2—5). 

With  the  number  five  Froebel  stops  on 
this  step.  One  to  five  are  sufficiently  known, 
even  to  the  child  three  years  old,  by  the 
number  of  his  fingers. 

The  productions  thus  far  accomplished  are 
now  combined.  The  child  draws,  side  by 
side  of  one  another,  lines  of  one  and  two 
lengths  (Fig.  6),  of  one,  two  and  three  lengths 
(Fig.  7),  of  one,  two,  three  and  four  lengths 
(Fig.  8),  and  finally  lines  of  one,  two,  three, 
four  and  five  lengths  (Fig.  9.)  It  always  forms 
by  so  doing  a  right-angled  triangle.  We 
have  noticed  already,  in  using  the  tablets,  that 
right-angled  triangles  can  lie  in  many  different 
ways.  The  triangle  (Fig.  9  and  10)  can  also 
assume  various  positions.  In  Fig.  10  the 
five  lines  stand  on  the  base  line — the  smallest 
is  the  first,  the  largest  the  last,  the  right  an- 
gle is  to  the  right  below.  In  Fig.  1 1  the  op- 
posite is  found — the  five  lines  hang  on  the 
base-line,  the  largest  comes  first,  the  smallest 
last,  and  the  right  angle  is  to  the  left  above. 
Figs.  12  and  13  are  forms  of  mediation  of  10 
and  II. 

The  child  should  be  induced  to  find  Figs. 
II  to  13  himself  Leading  him  to  understand 
the  points  of  Fig.  10  exactly,  he  will  have  no 
difficulty  in  representing  the  opposite.  Instead 
of  drawing  the  smallest  line  first,  he  will  draw 
the  longest ;  instead  of  drawing  it  downward, 
he  will  move  his  pencil  upward,  or  at  least 
begin  to  draw  on  the  line  which  is  bounded 
above,  and  thus  reach  11.  By  continued  re- 
flection, entirely  within  the  limits  of  his  capa- 
bilities, he  will  succeed  in  i^roducing  12  and  13. 


GUIDE   TO    KINDER- GARTNERS. 


49 


Thus,  by  a  different  way  of  combination  of 
five  perpendicular  lines,  four  forms  have  been 
produced,  consisting  of  equal  parts,  being, 
however,  unlike,  and  therefore  oppositionally 
alike. 

Each  of  these  figures  is  a  whole  in  itself. 
But  as  every  thing  is  always  part  of  a  larger 
whole,  so  also  these  figures  serve  as  elements 
for  more  extensive  formations. 

In  this  feature  of  Froebel's  drawing  method, 
in  which  we  progress  from  the  simple  to  the 
more  complicated  in  the  most  natural  and 
logical  manner,  unite  parts  to  a  whole  and 
recognize  the  former  as  members  of  the  latter, 
discover  the  like  in  opposites,  and  the  media- 
tion of  the  latter,  unquestionable  guarantee 
is  given  that  the  delight  of  the  child  will  be 
renewed  and  increased,  throughout  the  whole 
course  of  instruction.  Let  Figs.  lo — 13  be 
so  united  that  the  right  angles  connect  in 
the  center  (Fig.  14),  and  again  unite  them  so 
that  all  right  angles  are  on  the  outside  (Fig. 
15.)  Figs.  14  and  15  are  opposites.  No.  14 
is  a  square  with  filled  inside  and  standing  on 
one  corner;  No.  15  one  resting  on  its  base, 
with  hollow  middle.  In  14  the  right  angles 
are  just  in  the  middle;  in  15  they  are  the 
most  outward  corners.  In  the  forms  of  medi- 
ation (16  and  17),  they  are,  it  is  true,  on  the 
middle  line,  but  in  the  meantime  on  the  out- 
lines of  the  figures  formed.  In  the  other 
forms  of  mediation,  (Figs.  18,  19,  etc..)  they 
lie  altogether  on  the  middle  line  ;  but  two  in 
the  middle,  and  two  in  the  limits  of  the 
figure. 

Thus  we  have  again,  in  Figs.  18 — 22.  four 
forms  consisting  of  exactly  the  same  parts, 
which  therefore  are  equal  and  still  have  qual- 
ities of  opposites.  In  the  meantime,  they 
are  fit  to  be  used  as  simple  elements  of  fol- 
lowing formations.  In  Fig.  22,  they  are  com- 
bined into  a  star  with  filled  middle  ;  in  Fig. 
23,  it  is  shown  how  a  star  with  hollow  middle 
may  be  formed  of  them.  (The  Fig.  23,  on 
Plate  XXXVI.,  does  not  show  the  lower  part; 
on  Plate  XXIL,  Fig.  97,  Gift  Seventh,  the 
whole  star  is  shown.)     Here,  too,  numerous 


forms  of  mediation  may  be  produced,  but  we 
will  work  at  present  with  our  simple  elements. 

Owing  to  the  similarity  in  the  method  of 
drawing  to  that  employed  in  the  laying  of  the 
right  angled,  isosceles  triangle,  it  is  natural 
that  we  should  here  also  arrive  at  the  so-called 
rotation  figures,  by  grouping  our  triangles  with 
their  acute  angles  toward  the  middle  (Figs. 
24  and  25),  or  arrange  them  around  a  hollow 
square  (Figs.  26  and  27.) 

Figs.  28  and  29  are  forms  of  mediation 
between  24  and  25,  and  at  the  same  time 
between  14  and  15. 

All  these  forms  again  serve  as  material  for 
new  inventions.  As  an  example,  we  produce 
Fig.  30,  composed  of  Figs.  28  and  29. 

The  number  of  positions  in  which  our  orig- 
inal elements  (Figs.  10 — 13)  can  be  placed 
by  one  another,  is  herewith  not  exhausted  by 
far,  as  the  initiated  will  observe.  Simple  and 
easy  as  this  method  is  rendered  by  natural 
laws,  it  is  hardly  necessary  to  refer  to  the  tab- 
lets (Plates  XXI.  to  XXIX..)  which  will  sug- 
gest a  sufficient  number  of  new  motives  for 
further  combinations. 

As  previously  remarked,  the  slate  is  ex- 
changed for  a  drawing  book  as  soon  as  the  pro- 
gress of  the  child  warrants  this  change.  It 
affords  a  peculiar  charm  to  the  pupil  to  see  his 
productions  assume  a  certain  durability  and 
permanency  enabling  him  to  measure,  by  them, 
the  progress  of  growing  strength  and  ability. 

So  far  the  triangles  produced  by  cp  arrange- 
ment of  our  five  lines,  were  right-angled. 
Other  triangles,  however,  can  be  produced 
also.  This,  however,  requires  more  practice 
and  security  in  handling  the  pencil. 

Figs.  31  and  32  show  an  arrangement  of 
the  5  lines,  of  acute  angled  (equilateral)  tri- 
angles ;  Figs.  31  and  32  being  opposites. 
Their  union  gives  the  opposites  33  and  34 ; 
finally,  the  combination  of  these  two.  Fig.  35. 

In  the  last  three  figures  we  also  meet  now 
the  obtuse  angle.  This  finds  its  separate 
representation  in  the  manner  introduced  in 
Fig.  36  ;  opposition  according  to  position  is 
given  in  Fig.  37  ;  mediation  in  Figs.  38  and 


50 


GUIDE  TO   KINDER-GARTNERS. 


39,  and  the  combination  of  these  four  ele- 
ments in  one  rhomboid  in  Fig.  40.  The  four 
obtuse  angles  are  turned  inwardly.  Fig.  42, 
the  opposite  of  40,  is  produced  by  arranging 
the  triangles  in  such  a  manner  that  the  obtuse 
angles  are  turned  outwardly.  Fig.  41  pre- 
sents the  form  of  mediation.  Another  one 
might  be  produced  by  arranging  the  4  obtuse 
angled  triangles  represented  in  Nos.  36,  37, 
38,  and  39  in  such  a  manner  as  to  have  39 
left  above,  37  right  above,  36  left  below,  and 


38  right  below.     Thus  : 


39 
36" 


37 


It  is  evident  that  with  obtuse  angled  trian- 
gles, as  with  right  angled  triangles,  combina- 
tions can  be  produced.  Indeed,  the  pupil 
who  has.  grown  into  the  systematic  plan  of 
development  and  combination  will  soon  be 
enabled  to  unite  given  elements  in  manifold 
ways  ;  he  will  produce  stars  with  filled  and 
hollow  middle,  rotation  forms,  etc.,  and  his 
mental  and  physical  power  and  capacity  will 
be  developed  and  strengthened  greatly  by 
such  inventive  exercise. 

Side  by  side  with  invention  of  forms  of 
beauty  and  knowledge,  the  representation  of 
forms  of  life,  take  place,  in  free  individual  ac- 
tivity. The  child  forms,  of  lines  of  one  length, 
a  plate,  (Fig.  43.)  or  a  star,  (Fig.  44,)  of  lines 
of  one  and  two  lengths  a  cross,  (Fig.  45.)  of 
lines  up  to  4  lengths,  it  represents  a  coffee- 
mill,  (Fig.  46,)  and  employs  the  whole  material 
of  perpendicular  lines  at  his  command,  in  the 
construction  of  a  large  building  with  part  of  a 
wall  connected  with  it  (Fig.  47)  Equal 
consideration,  however,  is  to  be  bestowed 
upon  the  opposite  of  the  perpendicular, 

THE   HORIZONTAL   LINE. 
(PLATE    XXXIX.) 

The  child  learns  to  draw  lines  of  a  single 
length  below  each  other,  then  lines  of  2,  3,  4, 
and  5  lengths,  (Figs,  i — 5.)  It  arranges  them 
also  beside  each  other,  (Figs.  6 — 8)  unites 
lines  of  i  and  2  lengths,  (Fig.  9,)  of  i,  2,  and 
3  lengths,  (Fig.  10,)  of  i  to  4  lengths,  (Fig.  11.) 
finally  of  i   to  5  lengths,  thereby  producing 


the  right  angled  triangle  12,  its  opposite  13, 
and  forms  of  mediation  14  and  15.  The 
pupil  arranges  the  elements  into  a  square 
with  filled  middle,  (Fig.  16)  with  hollow  mid- 
dle, (Fig.  17)  produces  the  forms  of  mediation, 


c  I  a 
(Fig.  18,  — ,—  and 
b    d 


dlb 


-)  and  continues  to 


treat  the  horizontal  line  just  as  it  has  been 
taught  to  do  with  the  perpendicular.  (By  turn- 
ing the  Plates  XXXV.  to  XXXVIIL,  the 
figures  on  them  will  serve  as  figures  with  hori- 
zontal lines.)  Rotation  forms,  larger  figures, 
acute  and  obtuse  angled  triangles  can  be 
formed  ;  forms  of  beauty,  knowledge  and  life 
are  also  invented  here,  (Fig.  19,  adjustable 
lamp;  Fig.  20,  key  ;  Fig.  21.  pigeon  house  ;) 
and  after  the  child  has  accomplished  all  this,  it 
arrives  finally,  in  a  most  natural  way,  at  the 

COMBINATION  OF   PERPENDICULAR  AND 
HORIZONTAL   LINES. 

{plates  XL.  TO   XLILJ 

First,  lines  of  one  single  length  are  cpm- 
bined ;  we  already  have  four  forms  different 
as  to  position,  (Fig.  i.)  Then  follow  the 
combination  of  2,  3,  4,  5— fold  lengths,  (Figs. 
2 — 5)  with  each  of  which  4  opposites  as  to 
position  are  possible.  As  previously,  lines  of  i 
to  5— fold  lengths  are  united  to  triangles,  so 
now  the  angles  are  united  and  Fig.  6  is  pro- 
duced. Its  opposite,  7  and  the  forms  of  medi- 
ation, can  be  easily  found.  A  union  of  these 
four  elements  appears  in  the  square.  Fig.  8; 
opposite  Fig.  9.  In  Fig.  8,  the  right  angles  are 
turned  toward  the  middle,  and  the  middle  is 
full.  In  Fig.  9,  the  reverse  is  the  case.  Forms 
of  mediation  easily  found.     We  have  in  Figs. 


8  and  9  the  combinations 


c  b 

—  and  — 
b  c 


Let   the    following    be    constructed :    — 

a 


c 

"b 
b 

d 

a     c 

7' 7 

c     a 
a     c 

a     a 

"b'b" 
d 

"b* 

c     a 

7' 7 

b    d 

> 
c     a 

c    d 
7'b 

a    c 
c    a 

GUIDE  TO   KINDER  GARTNERS. 


5f 


If  perpendicular  and  horizontal  lines  can 
be  united  only  to  form  right  angles,  we  have 
previously  seen  that  perpendicular  as  well  as 
horizontal  lines  may  be  combined  to  obtuse 
and  acute  angled  triangles.  The  same  is  pos- 
sible, if  they  are  united.  Fig.  lo  gives  us  an 
example.  All  perpendicular  lines  are  so  ar- 
ranged as  to  form  obtuse  angled  triangles.  By 
their  combination  with  the  horizontal  lines, 
the  element  lo*  is  produced,  its  opposite  lo'', 
and  the  forms  of  mediation  lo*^  and  lo*^  whose 
combination  forms  Fig   ic 

As  in  Fig.  lo,  the  perpendicular  lines  form 
an  obtuse  angled  triangle,  so  the  horizontal 
lines,  and  finally  both  kinds  of  lines  can  at 
the  same  time  be  arranged  into  obtuse  angled 
triangles. 

Thus  a  series  of  new  elements  is  produced, 
whose  systematic  employment  the  teacher 
should  take  care  to  facilitate.  (The  scheme 
given  in  the  above  may  be  used  for  this 
purpose.) 

So  far  we  have  only  formed  angles  of  lines 
equal  in  length  ;  but  lines  of  unequal  lengths 
may  be  combined  for  this  purpose.  Exactly 
in  the  same  manner  as  lines  of  a  single  length 
were  treated,  the  child  now  combines  the  line 
of  a  single  length  with  that  of  two  lengths, 
then,  in  the  same  way,  the  line  of  two  lengths 
with  that  of  four  lengths,  that  of  three  with 
that  of  six,  that  of  four  with  that  of  eight,  and 
finally,  the  line  of  five  lengths  with  that  of  ten. 
The  combination  of  these  angles  affords  new 
elements  with  which  the  pupil  can  continue 
to  form  interesting  figures  in  the  already  well- 
known  manner.  Figs,  ii  and  12,  on  Plate 
XL.,  are  such  fundamental  forms ;  the  de 
velopment  of  which  to  other  figures  will  give 
rise  to  many  instructive  remarks.  These  fig- 
ures show  us  that  for  such  formations  the 
horizontal  as  well  as  the  perpendicular  line 
may  have  the  double  length.  Fig.  11  shows 
the  horizontal  lines  combined  in  such  a  way 
as  if  to  form  an  acute-angled  triangle.  They, 
howe%'er,  form  a  right-angled  triangle,  only  the 
right  angle  is  not,  as  heretofore,  at  the  end 
of  the  longest  line,  but  where?     An  acute- 


angled  triangle  would  result,  if  the  horizontal 
lines  were  all  two  net  squares  distant  from 
each  other.  Then,  however,  the  perpendicular 
lines  would  form  an  obtuse-angled  triangle. 

Important  progress  is  made,  when  we  com- 
bine horizontal  and  perpendicular  lines  in 
such  a  way  that  by  touching  in  two  points 
they  form  closed  figures,  squares  and  oblongs. 

First,  the  child  draws  squares  of  one- 
length's  dimension,  then  of  two-lengths,  of 
three,  four  and  five  lines.  These  are  combined 
then  as  perpendicular  lines  were  combined 
also  i^  with  2",  the  i",  2^  and  3^  etc.  These 
combinations  can  be  carried  out  in  a  perpen- 
dicular direction,  when  the  squares  will  stand 
over  or  under  each  other ;  or  in  horizontal, 
when  the  squares  will  stand  side  by  side ;  or, 
finally,  these  two  opposites  may  be  combined 
with  one  another. 

Fig.  13"  shows  as  an  example  a  combina- 
tion of  four  squares  in  a  horizontal  direction  ; 
13''  is  the  opposite  ;  c  and  d  are  forms  of  me- 
diation. 

In  Fig.  14',  squares  of  the  first,  second  and 
third  sizes  are  combined,  perpendicularly  and 
horizontally,  forming  a  right  angle  to  the 
right  below ;  b  is  the  opposite,  (angle  left 
above  ;)  c  and  d  are  forms  of  mediation.  The 
same  rule  is  followed  here  as  with  the  right 
angle  formed  by  single  lines.  The  simple 
elements  are  combined  with  each  other  into  a 
square  with  full  or  hollow  middle,  etc. ;  and 
from  the  new  elements  thus  produced  larger 
figures  are  again  created,  as  the  example  Fig. 
15,  Plate  XLL,  illustrates.  From  the  four 
elements  14"*""^,  the  figure  15"  and  its  opposite 
B  are  constructed,  (analogous  to  the  manner 
employed  with  Fig.  28.  Plate  XXXVII.,)  a  two- 
fold combination  of  which  resulted  in  Fig.  15. 
Squares  of  from  one  to  five  length  lines  of 
course  admit  of  being  combined  in  similar 
manner.  Each  essentially  new  element  should 
give  rise  to  a  number  of  exercises,  conditioned 
only  by  the  individual  ability  of  the  child.  It 
must  be  left  to  the'  faithful  teacher,  by  an 
earnest  observation  and  study  of  her  pupils, 
to  find  the  right  extent,  here  as  everywhere  in 


52 


GUIDE   TO    KINDER  GARTNERS. 


their  occupations.  Indiscriminate  skipping 
is  not  alio. ved,  neither  to  pupil  nor  teacher; 
each  following  production  must,  under  all  cir- 
cumstances be  derived  from  the  preceding  one. 

As  the  square  was  the  result  of  angles 
formed  of  lines  of  equal  length,  so  also  with 
the  oblong.  Here  too  the  child  begins  with 
the  simplest.  It  forms  oblongs,  the  base  of 
which  is  a  single  line,  the  heij^ht  of  which  is  a 
line  of  double  length.  It  reverses  the  case 
then.  Bise  line  2,  height  single  length.  Re- 
taining the  same  proportions,  it  progresses  to 
larger  oblongs,  the  height  of  which  is  double 
the  size  of  its  base,  and  vice  versa,  until  it 
has  reached  the  numbers  5  and  10. 

It  is  but  natural  that  these  oblongs,  stand- 
ing or  lying,  should  also  be  united  in  perpen- 
dicular, and  horizontal  directions.  Each  form 
thus  produced  again  assumes  four  different 
positions,  and  the  four  elements  are  again 
united  to  new  formations,  according  to  the 
rules  previously  explained.  Fig.  16'*  shows  an 
arrangement  of  standing  oblongs,  in  horizontal 
directions.  The  opposite  would  contain  the 
right  angle,  at  a  to  the  right  below — to  the 
left  above;  16'^  would  be  one  form  of  media- 
tion, a  second  one,  (opposite  of  16''.)  would 
have  its  right  angle  to  the  right  above. 

Fig.  17  shows  a  combination  of  lying  ob- 
longs, in  a  perpendicular  direction.  Fig.  18, 
shows  oblongs  in  perpendicular  and  horizon- 
tal directions.  Fig.  19,  a  combination  of  stand 
ing  and  lying  oblongs,  the  former  being  ar- 
ranged perpendicularly,  the  latter,  horizon 
tally. 

In  Fig.  20,  we  find  standing  oblongs  so 
combined  that  the  form  represents  an  acute 
angled  triangle  :  a  and  b  are  the  only  possible 
opposites  in  the  same. 

These  few  examples  may  suffice  to  indicate 
the  abundance  of  forms  which  may  be  con- 
structed with  such  simple  material  as  the 
horizontal  and  perpendicular  lines,  from  i  to 
5  lengths,  (and  double.) 

It  is  the  task  of  the  educator  to  lead  the 
learner  to  detect  the  elements,  logically,  in 
order  to  produce  with  them,  new  forms   in 


unlimited  numbers,  within  the  boundaries  of 
the  laws  laid  down  for  this  purpose. 

But  even  without  using  these  elements,  the 
child  will  be  able,  owing  to  continued  practice, 
to  represent  manifold  forms  of  life  and  beauty, 
partly  by  its  own  free  invention,  partly  by 
imitating  the  objects  it  has  seen  before.  As 
samples  of  the  former,  Plate  XLII.,  Fig.  27, 
shows  a  cross.  Fig.  29,  a  triumphal  gate.  Fig. 
30,  a  wind-mill,  of  the  latter,  Fig.  21 — 24,  and 
28,  show  samples  of  borders  ;  Fig.  25  and  26, 
show  other  simple  embellishments.  As  the 
perpendicular  line  conditioned  its  opposite, 
the  horizontal  line,  both  again  condition  their 
mediation. 

THE   OBLIQUE   LINE. 

(plates  xliii.  to  xi.v.) 

Our  remarks  here  can  be  brief  as  the  ope- 
rations are  nothing  but  a  repetition  of  those 
in  connection  with  the  perpendicular  line. 

The  child  practices  the  drawing  of  lines 
from  I  to  5  lengths,  (Plate  XLIII.,  i  to  5,) 
and  combines  these,  receiving  thereby  4  op- 
positionally  equal  right  angled  triangles,  (Fig. 
6 — 9,)  of  which  it  produces  a  square,  (Fig.  10.) 
its  opposite,  (Fig.  11.)  forms  of  mediation,  and 
finally  large  figures. 

Then  the  lines  are  arranged  into  obtuse 
angles,  and  the  same  process  gone  through 
with  them. 

With  these,  as  in  Fig.  13,  its  opposite  16, 
and  its  forms  of  mediation,  14  and  15,  the 
obtuse  angles  will  be  found  at  the  perpendic- 
ular middle  line,  or  as  in  17,  at  the  horizontal 
middle  line.  By  a  combination  of  15  and  17, 
we  produce  a  star,  19.  Finally  we  have  also, 
reached  here  the  formation  of  the  acute 
angled  triangle,  (Fig.  18.)  '1  he  oblique  line 
presents  particular  richness  in  forms,  as  it 
may  be  a  line  of  various  degrees  of  inclina- 
tion. It  is  an  oblique  of  the  first  degree 
whenever  it  appears  as  the  diagonal  of  a 
square,  as  in  Figs,  i — 19.  \^"hen  it  appears 
as  the  diagonal  of  an  oblong,  it  is  either  an 
oblique  of  the  2d,  3d.  4th,  or  5th  degree,  ac 
cording  to  the  proportions  of  the  base  line, 


GUIDE     TO     KINDER-GARTNERS. 


53 


and  height  of  tlie  oblong,  i  to  2,  i  to  3,  i  to 
4,  I  to  5. 

In  Fig.  20",  obliques  of  the  second  degree 
are  united  to  a  right-angled  triangle.  20''  is 
the  opposite,  20*^  and  d  form  mediations. 

In  Fig.  21,  the  same  lines  are  united  in  an 
obtuse  angled  triangle.  In  Fig.  22,  they  finally 
form  an  acute  angle. 

In  all  these  cases,  the  obliques  were  diag- 
onals of  standing  oblongs.  I'hey  may  just  as 
well  be  diagonals  of  lying  oblongs.  Fig.  23, 
in  which  obliques  from  the  first  to  the  fifth 
degree  are  united,  will  illustrate  this.  The 
obliques  are  here  arranged  one  above  the 
other.  In  Fig.  24,  the  members  a  and  b  show 
a  similar  combination ;  the  obliques,  however, 
are  arranged  beside  one  another  ;  the  mem- 
bers, c  and  d,  are  formed  of  diagonals  of  stand- 
ing oblongs. 

Obliques  of  various  grades  can  be  united 
with  one  point,  when  the  element  a  in  Fig.  25, 
will  be  produced,  which  requires  the  other 
elenents,  b,  c,  and  d,  to  form  this  figure,  the 
opposite  of  which  would  have  to  be  formed 

b    d 

according  to  the  formula,  —  — ,  beside  which 


b    d 


the  forms  of  mediation  would  appear  as 

d{b 
(Fig.  26)  and  — , — . 
a  I  c 

As  in  this  case,  lying  figures  are  produced, 
standing  ones  can  be  produced  likewise. 
Each  two  of  the  elements  thus  received  may 
be  united,  so  that  all  obliques  issue  from  one 
point,  as  in  Fig.  27,  and  in  its  opposite,  Fig.  28. 

An  oppositional  combination  can  also  take 
place,  so  that  each  two  lines  of  the  same 
grade  meet,  (Fig.  29.)  The  combination  of 
■obliques  with  obliques  to  angles,  to  squares 
and  oblongs  now  follow,  analogous  to  the 
method  of  combining  oblongs,  perpendicular 
and  horizontal  lines.  Finally  the  combination 
of  perpendicular  and  oblique,  horizontal  and 
oblique  lines  to  angles,  rhombus  and  rhomboid 
is  introduced. 

With  these,  the  child  tries  his  skill  in  pro- 


ducing forms  of  life:  Fig.  40,  gate  of  a  for- 
tress; 41,  church  with  school-house  and  cem- 
etery wall,  and  forms  of  beauty :  Figs.  30 — 39. 
The  task  of  the  Kinder  Garten  and  the 
teacher  has  been  accomplished,  if  the  child 
has  learned  to  manage  oblique  lines  of  the 
first  and  second  degree  skillfully.  All  given 
instruction  which  aimed  at  something  beyond 
this,  was  intended  for  the  study  of  the  teacher 
and  the  Primary  Department,  which  is  still 
more  the  case  in  regard  to — 

THE   CURVED    LINE. 

(PLATK   XLVI.) 

Simply  to  indicate  the  progress,  and  to  give 
Froebel's  system  of  instruction  in  drawing 
complete,  we  add  the  following,  and  Plate 
XLVI.  in  illustration  of  it 

First,  the  child  has  to  acquire  the  ability  to 
draw  a  curved  line.  The  simplest  curved  line 
is  the  circle,  from  which  all  others  may  be 
derived. 

However,  it  is  diflficult  to  draw  a  circle,  and 
the  net  on  slate  and  paper  do  not  afford  suffi- 
cient help  and  guide  for  so  doing.  But  on 
the  other  hand,  the  child  has  been  enabled  to 
draw  squares,  straight  and  oblique  lines,  and 
with  the  assistance  of  these  it  is  not  difficult 
to  find  a  number  of  points  which  lie  on  the 
periphery  of  a  circle  of  given  size. 

It  is  known  that  all  corners  of  a  quadrangle 
(square  or  oblong)  lie  in  the  periphery  of  a 
circle  whose  diameter  is  the  diagonal  of  the 
quadrangle.  In  the  same  manner  all  other 
right  angles  constructed  over  the  diameter, 
are  periphery  angles,  affording  a  point  of  the 
desired  circular  line.  It  is  therefore  nec- 
essary to  construct  such  right  angles,  and  this 
can  be  done  very  readily  with  the  assistance 
of  obliques  of  various  grades. 

Suppose  we  draw  from  point  a  (Fig.  i)  an 
oblique  of  the  third  degree,  as  the  diagonal 
of  a  standing  oblong  ;  draw  then,  starting 
from  point  c,  an  oblique  of  the  third  degree,  as 
diagonal  of  a  lying  oblong,  and  continue  both 
these  lines.  They  will  meet  in  point  a,  and 
there  form  a  right  angle 


54 


GUIDE    TO     KINDER-GARTNERS. 


All  obliques  of  the  same  degree,  drawn 
from  opposite  points,  will  do  the  same  as 
soon  as  the  one  approaches  the  perpendicular 
in  the  same  proportion  in  which  the  other 
comes  near  the  horizontal,  or  as  soon  as  the 
one  is  the  diagonal  of  a  standing,  the  other 
of  a  lying  oblong. 

The  lines  Aa  and  Cc  are  obliques  of  the 
third,  Ab  and  Cb  of  the  second,  Af  and  C/ 
of  the  third  degree,  etc.,  etc.  In  this  manner 
it  is  easy  to  find  a  number  of  points,  all  of 
which  are  points  in  the  circular  line,  intended 
to  be  drawn.  Two  or  three  of  them  over 
each  side,  will  suffice  to  facilitate  the  drawing 
of  the  ciRCUMscribing  circle,  (Fig.  2  )  In  like 
manner,  the  iNXERScribing  circle  will  be  ob- 
tained by  drawing  the  middle  transversals  of 
the  square,  (Fig.  3,)  and  constructing  from 
their  end-points  angles  in  the  previously  de- 
scribed manner- 
After  the  pupil  has  obtained  a  correct  idea 
of  the  size  and  form  of  the  circle,  whose  ra- 
dius may  be  oi  from  one  to  five  lengths,  it 
will  divide  the  same  in  half  and  quarter  cir- 
cles, producing  thereby  the  elements  for  its 
farther  activity. 

The  course  of  instruction  is  here  again  the 
same  as  that  in  connection  with  the  perpen- 
dicular line.  The  pupil  begins  with  quarter 
circles,  radius  of  which  is  of  a  single  length. 
Then  follow  quarter  circles  with  a  radius  of 
from  two  to  five  lengths.  'By  arrangement  of 
these  five  quarter  circles,  four  elements  are 
produced,  which  are  treated  in  the  same  man- 
ner as  the  triangles  produced  by  arrangement 
of  five  straight  lines.  The  segments  may  be 
parallel,  and  the  arrangement  may  take  place 
in  perpendicular  and  horizontal  direction,  (Fig. 
4  and  5,)  or  they  may,  like  the  obliques  of  va- 
rious degrees,  meet  in  one  point,  as  in  Fig.  8, 
of  which  Figs.  4  and  5  are  examples. 


Fig.  6  represents  the  combination  of  the 
elements  a  and  ^  as  a  new  element ;  Fig.  7, 
the  combination  of  d  and  c  In  Fig.  8  the 
arrangement  finally  takes  place  in  oblique 
direction,  and  all  lines  meet  in  one  point. 

The  quarter  circle  is  followed  by  the  half 
circle  9,  10,  11  ;  then  the  three  fourths  circle 
(Fig  12),  and  the  whole  circle,  as  shown  in 
Fig    13- 

With  the  introduction  of  each  new  line,  the 
same  manner  of  proceeding  is  observed. 

Notwithstanding  the  brevity  with  which  we 
have  treated  the  subject,  we  nevertheless 
believe  we  have  presented  the  course  of  in- 
struction in  drawing  sufficiently  clearly  and 
forcibly,  and  hope  that  by  it  we  have  made 
evident : 

1.  That  the  method  described  here  is  per- 
fectly adapted  to  the  child's  abilities,  and  fit 
to  develop  them  in  the  most  logical  manner  ; 

2.  That  the  abundance  of  mathematical 
perceptions  offered  with  it,  and  the  constant 
necessitv  for  combining  according  to  certain 
laws,  can  not  fail  to  surely  exert  a  wholesome 
influence  in  the  mental  development  of  the 
pupil  ; 

3.  That  the  child  thus  prepared  for  future 
instruction  in  drawing,  will  derive  from  such 
instruction  more  benefit  than  a  child  prepared 
by  any  other  method. 

Whosoever  acknowledges  the  importance 
of  drawing  for  the  future  life  of  the  pupil — 
may  he  be  led  therein  by  its  significance  for 
industrial  purposes,  or  aesthetic  enjoyment, 
which  latter  it  may  afford  even  the  poorest ! — 
will  be  unanimous  with  us  in  advocating  an 
early  commencement  of  this  branch  of  in- 
struction with  the  child. 

If  there  be  any  skeptics  on  this  point,  let 
them  try  the  experiment,  and  we  are  sure  they 
will  be  won  over  to  our  side  of  the  question. 


THE  ELEVENTH  AND  TWELFTH  GIFTS. 


MATERIAL    FOR    PERFORATING    AND    EMBROIDERING. 


(PLATF.S     XLVII.     TO     L.) 


It  is  claimed  by  us  that  all  occupation  ma- 
terial presented  by  Froebel.  in  the  Gifts  of  the 
Kinder-Garten,  are,  in  some  respects,  related 
to  each  other,  complementing  one  another. 
What  logical  connection  is  there  between  the 
occupation  of  perforating  and  embroidering, 
introduced  with  the  present  and  the  use  of 
the  previously  introduced  Gifts  of  the  Kinder- 
Garten  ?  This  question  may  be  asked  by 
some  superficial  enquirer.  Him  we  answer 
thus  :  In  the  first  Gifts  of  the  Kinder  Garten, 
the  solid  mass  of  bodies  prevailed  ;  in  the  fol- 
lowing ones  the  plane ;  then  the  embodied  line 
was  followed  by  the  drarvn  line,  and  the  occu 
pation  here  introduced  brings  us  down  to  the 
point.  With  the  introduction  of  the  per- 
forating paper  and  pricking  needle,  we  have 
descended  to  the  smallest  part  of  the  whole — 
the  extreme  limit  of  mathematical  divisibility ; 
and  in  a  playing  manner,  the  child  followed 
us  unwittingly,  on  this,  in  an  abstract  sense, 
difficult  journey. 

The  material  for  these  occupations  is  a 
piece  of  net  paper,  which  is  placed  upon 
some  layers  of  soft  blotting  paper.  The 
pricking  or  perforating  tool  is  a  rather  strong 
sewing  needle,  fastened  in  a  holder  so  as  to 
project  about  one-fourth  of  an  inch.  Aim  of 
the  occupation  is  the  production  of  the  beau- 
tiful, not  only  by  the  child's  own  activity,  but 
by  its  own  invention.  Steadiness  of  the  eye 
and  hand  are  the  visible  results  of  the  occu- 
pation which  directly  prepares  the  pupil  for 
various  kinds  of  manual  labor.  The  per- 
forating,  accompanied    by    the    use    of    the 


needle  and  silk,  or  worsted,  in  the  way  em- 
broidery is  done,  it  is  evident  in  what  direc- 
tion the  faculty  of  the  pupil  may  be  developed. 

The  method  pursued  with  this  occupation 
is  analogous  to  that  employed  in  the  drawing 
department.  Starting  from  the  single  point, 
the  child  is  gradually  led  through  all  the 
various  grades  of  difficulty  ;  and  from  step  to 
step  its  interest  in  the  work  Avill  increase, 
especially  as  the  various  colors  of  the  em- 
broidered figures  add  much  to  their  liveliness, 
as  do  the  colored  pencils  in  the  drawing 
department. 

The  child  first  pricks  perpendicular  lines 
of  two  and  three  lengths,  then  of  four  and  five 
lengths,  (Figs.  2  and  3.)  They  are  united  to 
a  triangle,  opposites  and  forms  of  mediation 
are  found,  and  these  again  are  united  into 
squares  with  hollow  and  filled  middle,  (Figs. 
4  and  5.)  The  horizontal  line  follows,  (Figs. 
6 — 8,)  then  the  combination  of  perpendicu- 
lar and  horizontal  to  a  right  angle  in  its  four 
oppositionally  equal  positions,  (Figs.  9 — 12.) 
The  combination  of  the  four  elements  present 
a  vast  number  of  small  figures.  If  the  exter- 
nal point  of  the  angle  of  9  and  10  touch  one 
another,  the  cross  (Fig.  13)  is  produced;  if 
the  end  points  of  the  legs  of  these  figures 
touch,  the  square  is  made,  (Fig.  14.)  By 
repeatedly  uniting  9  and  12  Fig.  15  is  pro- 
duced, and  by  the  combination  of  all  four 
angles  Figs.  16  and  17.  According  to  the 
rules  followed  in  laying  figures  with  tab 
lets  of  Gift  Seven,  and  in  drawing,  or  by  a 
simple  application  of  the  law  of  opposites,  the 


GUIDE  TO   KINDER  GARTNERS. 


child  will  produce  a  large  number  of  other 
figures. 

The  combination  of  lines  of  i  and  2  lengths 
is  then  introduced,  and  standing  and  lying 
oblongs  are  formed,  (Figs.  18  and  19,)  etc. 
The  school  of  perforating  per  se,  has  to  con- 
sider still  simple  squares  and  lying  and 
standing  oblongs,  consisting  of  lines  of  from 
2  to  5  lengths.  In  order  no:  to  repeat  the 
same  form  too  often,  we  introduce  in  Figs. 
21 — 31  a  series  of  less  simple}  containing, 
however,  the  fundamental  forms,  showing  in 
the  meantime  the  combination  of  lines  of 
various  dimensions. 

In  a  similar  way,  the  oblique  line  is  now 
introduced  and  employed.  The  child  pricks 
it  in  various  directions,  commencing  with  a 
one  length  line,  (Figs.  32 — 35.)  combines  it  to 
angles,  (Figs.  36—39,)  the  combination  of 
which  will  again  result  in  many  beautiful 
forms.  Then  follows  the  perforating  of  ob- 
lique lines  of  from  2  to  5  lengths,  (a  single 
length  containing  up  to  seven  points,)  which 
are  employed  for  the  representation  of  bor- 
ders, corner  ornaments,  etc.,  (Figs.  42 — 45, 
61.)  The  oblique  of  the  second  degree  is 
also  introduced,  as  shown  in  Figs.  46  and  47, 
and  the  peculiar  formations  in  Figs.  48  —  51. 

Finally,  the  combination  of  the  oblique 
with  the  perpendicular  line,  (Figs.  52  and  54,) 
and  with  the  horizontal,  (Figs.  53  and  55,)  or 
with  both  at  the  same  time,  (Figs.  56 — 60,); 
takes  place.  The  conclusion  is  arrived  at  in 
the  circle  (Fig.  62)  and  the  half  circle  (Figs. 
63—69.) 

All  these  elements  may  be  combined  in 
the  most  manifold  manner,  and  the  inventive 
activity  of  the  pupil  will  find  a  large  field  in 
producing  samples  of  borders,  corner-pieces, 
frames,  reading  marks,  etc  ,  etc. 

When  it  is  intended  to  produce  anything  of 
a  more  complicated  nature,  the  pattern  should 
be  drafted  by  pupil  or  teacher  upon  the  net 
paper  previous  to  pricking.  In  such  cases, 
it  is  advisable  and  productive  of  pleasure  to 
the  pupils,  if  beneath  the  perforating  paper 
another  one  doubly  folded  is  laid,  to  have  the 


pattern  transferred  by  perforation  upon  this 
paper  in  various  copies.  Such  little  produc- 
tions may  be  used  for  various  purposes,  and 
be  presented  by  the  children  to  their  friends 
on  many  occasions.  To  assist  the  pupils  in 
this  respect,  it  is  recommended  that  simple 
drawings  be  placed  in  the  hands  of  the  pupils, 
which,  owing  to  their  little  ability,  they  cer- 
tainly could  not  yet  produce  by  drawing,  but 
which  they  can  well  trace  with  their  per- 
forating tool.  These  drawings  should  repre- 
sent objects  from  the  animal  and  vegetable 
kingdoms,  and  may  thus  be  of  great  service 
for  the  mental  development  of  the  children. 
The  slowly  and  carefully  perforated  forms 
and  figures  will  undoubtedly  be  more  last- 
ingly impressed  upon  the  mind  and  longer 
retained  by  the  memory,  than  if  they  were 
only  described  or  hurriedly  looked  at.  Plate 
XLIX.  presents  a  few  of  such  pictures,  which 
can  easily  be  multiplied. 

A  particular  explanation  is  required  for 
Fig.  84,  on  Plate  L.  In  this  figure  are  con- 
tained shaded  parts,  indicating  plastic  forms, 
which  so  far  have  not  been  introduced,  all 
previous  figures  presenting  mere  outlines  to 
be  perforated.  It  is  supposed  to  be  known 
that  each  prick  of  the  needle  causes  some- 
what of  an  elevation  on  the  reverse  (wrong 
side)  of  the  paper.  If  a  number  of  very  fine, 
scarcely  visible  pricks  are  made  around  a 
certain  point,  an  elevated  place  will  be  the 
result,  so  mu  :h  more  observable,  the  larger 
the  number  of  pricks  concentrated  on  the 
spot.  In  this  wise  it  is  possible  to  represent 
certain  parts  of  a  design  as  standing  out  in 
relief  It  is  understood  that  very  young  chil- 
dren could  not  well  succeed  in  such  kind  of 
v.ork.  The  older  ones  find  material  in  Figs. 
72,  74  and  76  to  try  their  skill  in  this  direc- 
tion, and  thereby  prepare  themselves  for  fig- 
ures like  84. 

All  figures  of  Plates  XXXIX ,  XLIL,  and 
XLIX.  may  well  be  used  for  samples  of  per- 
forating and  embroidering. 

It  should  be  mentioned  that  the  embroider- 
ing does  not  begin  simultaneously  with  the 


GUIDE    TO    KINDER  GARTNERS. 


57 


perforating,  but  only  after  the  children  have 
acquired  considerable  skill  in  the  last  named 
occupation.     For  purposes  of 

EMBROIDERING, 
The  same  net  paper  which  was  used  for  exer- 
cises in  perforating  may  be  employed,  by  fill- 
ing out  the  intervals  between  the  holes  with 
threads  of  colored  silk  or  worsted.  It  will  be 
sufficient  for  this  purpose  to  combine  the 
points  of  one  net  square  only,  because  other- 
wise the  stitches  would  become  too  short  to 
be  made  with  the  embroidery  needle  in  the 
hands  of  children  yet  unskilled.  For  work,  to 
be  prepared  for  a  special  purpose,  the  perfor- 
ated pattern  should  be  transferred  upon  stiff 
paper  or  bristol -board. 

Course  of  instruction  just  the  same  as  with 
perforating. 

Experience  will  show  that  of  the  figures 
contained  on  our  plates,  some  are  more  fit  for 
perforating,  others  better  adapted  for  embroid- 
ering. Either  occupation  leads  to  peculiar 
results.  Figures  in  which  strongly  rounded 
lines  predominate  may  be  easily  perforated, 
but  with  difficulty,  or  not  at  all  be  embroid- 
ered, as  Figs.  75  and  77.  By  the  process  of 
embroidering,  however,  plain  forms,  as  stars, 
and  rosettes,  are  easily  produced,  which  could 
hardly  be  represented,  or,  at  best,  very  imper- 
fectly only,  by  the  perforating  needle.  Figs. 
87 — 92.  and  Fig.  39  on  Plate  XLII.  are  ex- 
amples of  this  kind. 

To  develop  the  sense  of  color  in  the  chil- 
dren, the  paper  on  which  they  embroider, 
should  be  o(  all  the  various  shades  and  hues, 
through  the  whole  scale  of  colors.  If  the 
paper  is  gray,  blue,  black,  or  green,  let  the 
worsted  or  silk  be  of  a  rose  color,  white,  or- 
ange or  red,  and  if  the  pupil  is  far  enough 
advanced  to  represent  objects  of  nature,  as 
fruit,  leaves,  plants,  or  animals,  it  will  be  very 
proper   to    use    in    embroidering,  the  colors 


shown  by  these  natural  objects.  Much  can 
be  thereby  accomplished  toward  an  early  de- 
velopment of  appreciation  and  knowledge  of 
color,  in  which  grown  people,  in  all  countries 
are  often  sadly  deficient.  It  has  appeared  to 
some,  as  if  this  occupation  is  less  useful  than 
pleasurable.  Let  them  consider  that  the  ordi- 
nary seeing  of  objects  already  is  a  difficult 
matter,  nay,  really  an  art,  needing  .long  prac- 
tice. Much  more  difficult  and  requiring  much 
more  careful  exercise,  is  a  true  and  correct 
perception  of  color. 

If  the  beatctiful  is  introduced  at  all  as  a 
means  of  education — and  in  Froebel's  institu- 
tions it  occupies  a  prominent  place — it  should 
approach  the  child  in  various  ways  j  not  only 
mform,  but  in  color,  and  tone  also.  To  insure 
the  desired  result  in  this  direction,  we  begin 
in  the  Kinder  Garten,  where  we  can  much 
more  readily  make  impressions  upon  the 
blank  minds  of  children,  than  at  a  later  pe- 
riod when  other  influences  have  polluted  their 
tastes. 

For  this  reason,  we  go  still  another  step 
farther,  and  give  the  more  developed  pupil  a 
box  with  the  three  fundamental  colors,  show- 
ing him  their  use,  in  covering  the  perforated 
outlines  of  objects  with  the  paint  Children 
like  to  occupy  them.selves  in  this  manner,  and 
show  an  increased  interest,  if  they  first  pro- 
duce the  drawing  and  are  subsequently  al- 
lowed to  use  the  brush  for  further  beautifying 
their  work. 

We  only  give  three  fundamental  colors,  in 
order  not  to  confound  the  beginner  by  need- 
less multiplicity,  as  also  to  teach  how  the  sec- 
ondary colors  may  be  produced  by  mixing  the 
primar)'. 

The  perforating  and  embroidering  are  be- 
gun with  the  children  in  the  Kinder-Garten, 
W'hen  they  have  become  sufficiently  prepared 
for  the  perception  of  forms  by  the  use  of  their 
building-blocks  and  staffii. 


THE  THIRTEENTH  GIFT. 


MATERIAL    FOR    CUTTING    PAPER    AND    MOUNTING    PIECES    TO    PRODUCE 

FIGURES    AND    FORMS. 

(plates     LI.    TO     LVIIL) 


The  labor,  or  occupation  alphabet,  pre- 
sented by  Froebel  in  his  system  of  education, 
cannot  spare  the  occupation,  now  introduced 
— the  cutting  of  paper — the  transmutation  of 
the  material  by  division  of  its  parts,  notwith- 
standing the  many  apparently  well  founded 
doubts,  whether  scissors  should  be  placed  into 
the  hands  of  the  child  at  such  an  early  age. 
It  will  be  well  for  such  doubters  to  consider : 
Firstly,  that  the  scissors  which  the  children 
use,  have  no  sharp  points,  but  are  rounded  at 
their  ends,  by  which  the  possibilities  of  doing 
harm  with  them  are  greatly  reduced  Sec 
ondly,  it  is  expected  that  the  teacher  employs 
all  possible  means  to  watch  and  superintend 
the  children  with  the  utmost  care  during  their 
occupation  with  the  scissors.  Thirdly,  as  it 
can  never  be  prevented,  that,  at  least,  at  times 
scissors,  knives  and.  similar  dangerous  objects 
may  fall  into  the  hands  of  children,  it  is  of 
great  importance  to  accustom  them  to  such, 
by  a  regular  course  of  instruction  in  their  use, 
which,  it  may  be  expected  will  certainly  do 
something  to  prevent  them  from  illegitimately 
applying  them  for  mischievous  purposes. 

By  placing  material  before  them  from  which 
the  child  produces,  by  cutting  according  to 
certain  laws,  highly  interesting  and  beautiful 
forms,  their  desire  of  destroying  with  the  scis- 
sors will  soon  die  out,  and  they,  as  well  as 
their  parents,  will  be  spared  many  an  unpleas- 
ant experience,  incident  upon  this  childish  in- 
stinct, if  it  were  left  entirely  unguided. 

As  material  for  the  cutting,  we  employ  a 
squ'ire  piece  of  paper  of  the  size  of  one  six- 


teenth sheet,  similar  to  the  folding  sheet. 
Such  a  sheet  is  broken  diagonally,  (Plate 
TXIX.,  Fig.  5  )  the  right  acute  angle  placed 
upon  the  left,  so  as  to  produce  four  triangles 
resting  one  upon  another.  Repeating  the  same 
proceeding,  so  that  by  so  doing  the  two  upper 
triangles  will  be  folded  upwards,  the  lower 
ones  downwards  in  the  halving  line,  eight 
triangles  resting  one  upon  another,  will  be 
produced,  which  we  use  as  our  first  funda- 
mental form.  This  fundmnental form  is  held, 
in  all  exercises,  so  that  the  open  side,  where  no 
plane  connects  with  another  is  always  turned 
toward  the  left. 

In  order  to  accomplish  a  sufficient  exact- 
ness in  cutting,  the  uppermost  triangle  con- 
tains, (or  if  it  does  not,  is  to  be  provided  with) 
a  kind  of  net  as  a  guide  in  cutting.  Dotted 
lines  indicate  on  our  plates  this  net  work. 

The  actixity  itself  is  regulated  according 
to  the  law  of  opposites.  We  commence  with 
the  perpendicular  cut,  come  to  its  opposite, 
the  horizontal  rrd  finally  to  the  mediation  of 
both,  the  oblique 

Plates  51 — 53  indicate  the  abundance  of 
cuts  which  may  be  developed  according  to 
this  method  and  it  is  advisable  to  arrange  for 
the  child  a  selection  of  the  simpler  elements 
into  a  school  of  cutting. 

The  following  selection  presents,  almost 
always,  two  opposites  and  their  combination, 
or  leaves  out  one  of  the  former,  as  is  the  case 
with  the  horizontal  cut,  wherever  it  does  not 
produce  anything  essentially  new. 

a.      Perpendicular  cuts,  2.  3,  4 — 5    6,  7. 


GUIDE    TO    KINDER- GARTNERS. 


59 


b  Horizontal  cuts,  8,  9— (above  ;  above 
and  below). 

c.     Perpendicular   and    horizontal,   18,   19, 
20 — 21,  22,  23. 
,     d.     Oblique  cuts,  34,  35—36,  37,  38- 

e.     Oblique  and  perpendicular,  51,  52,  53, 

—54-  55,  56—58.  59,  60. 
/     Oblique  and  horizontal.  65,  66,  67. 

g.  Half  oblique  cuts,  where  the  diagonals 
of  standing  and  lying  oblongs,  formed  of  two 
net  squares  serve  as  guides — 117,  118,  119 — 
121.  122,  123 — 125,  126,  127. 

Here  ends  the  school  of  cutting,  per  se^  for 
the  first  fundamental  form,  the  right  angled 
triangle.  The  given  elements  may  be  com- 
bined in  the  most  manifold  manner,  as  this 
has  been  sufficiently  carried  out  in  the  forms 
on  our  plates. 

The  fundamental  form  used  for  Plates  LIV. 
and  LV.  is  a  six  fold  equilateral  triangle.  It 
also  is  produced  from  the  folding  sheet,  by 
breaking  it  diagonally,  halving  the  middle  of 
the  diagonal,  dividing  again  in  three  equal 
parts  the  angle  situated  on  this  point  of  halv- 
ing. The  angles  thus  produced  will  be  an- 
gles of  60  degrees.  The  leaf  is  folded  in  the 
legs  of  these  angles  by  bending  the  one  acute 
angle  of  the  original  triangle,  upwards,  the 
other  downwards.  By  cutting  the  protruding 
corners,  we  shall  have  the  desired  form  of  the 
six  fold  equilateral  triangle,  in  which  the  en- 
tirely open  side  serves  as  basis  of  the  triangle. 
The  net  for  guidance  is  formed  by  division  of 
each  side  in  four  equal  parts,  uniting  the  points 
of  division  of  the  base,  by  parallel  lines  with 
t'le  sides,  and  drawing  of  a  perpendicular 
from  the  upper  point  of  the  triangle  upon  its 
base.  It  is  the  oblique  line,  particularly  which 
is  introduced  here.  The  designs  and  patterns 
from  133 — 145,  will  suffice  for  this  purpose. 
The  same  fundamental  form  is  used  for  prac 
tising  and  performing  the  circular  cuts,  al- 
though the  right  angular  fundamental  form 
may  be  used  for  the  same  purpose.  Both  find 
their  application  subsequently,  in  a  sphere  of 
development  only,  after  the  child  by  means 
of  the  use  of  the  half  and  whole  rings,  and 


drawing,  has  become  more  familiar  with  the 
curved  line.  These  exercises  require  great 
facility  in  handling  the  scissors,  besides,  and 
are,  therefore,  only  to  be  introduced  with 
children,  who  have  been  occupied  in  this  de- 
partment quite  a  while.  For  such  it  is  a  cap- 
ital employment,  and  they  will  find  a  rich 
field  for  operation,  and  produce  many  an  in- 
teresting and  beautiful  form  in  connection 
with  it.  The  course  of  development  is  indi- 
cated in  figures  164 — 172. 

After  the  child  has  been  sufficiently  intro- 
duced into  the  cutting  school,  in  the  manner 
indicated  in  the  above ;  after  his  fantasy 
has  found  a  definite  guidance  in  the  ever-re- 
peated application  of  the  law,  which  protects 
him  against  unbounded  option  and  choice,  it 
will  be  an  easy  task  to  him,  and  a  profitable 
one,  to  pass  over  to  free  invention,  and  to 
find  in  it  a  fountain  of  enjoyment,  ever  new, 
and  inexhaustibly  overflowing.  To  let  the 
child,  entirely  without  a  guide,  be  the  master 
of  his  own  free  will,  and  to  keep  all  discipline 
out  of  his  way,  is  one  of  the  most  dangerous 
and  most  foolish  principles  to  which  a  misun- 
derstood love  of  children,  alone,  could  bring 
us.  This  absolute  freedom  condemns  the 
children,  too  soon,  to  the  most  insupportable 
annoyance.  All  that  is  in  the  child  should  be 
brought  out  by  means  of  external  influence. 
To  limit  this  influence  as  much  as  possible  is  not 
to  suspend  it.  Froebel  has  limited  it,  in  a  most 
admirable  way  by  placing  this  guidance  into  the 
child  itself,  as  early  as  possible  j  that  from  one 
single  incitement  issues  a  number  of  others, 
within  the  child,  by  accustoming  it  to  a  lawful 
and  regulated  activity  from  its  earliest  youth. 

With  the  first  perpendicular  cut,  which  we 
made  into  the  sheet  (Fig.  i,)  the  whole  course 
of  development,  as  indicated  in  the  series  of 
figures  up  to  No.  132  is  given,  and  all  subse- 
quent inventions  are  but  simple,  natural  com- 
binations of  the  element  presented  in  the 
'^schofliy  Thus  a  logical  connection  prevails 
in  these  formations,  as  among  all  other  means 
of  education,  hardly  any  but  mathematics 
mav  afford. 


6o 


GUIDE    TO    KINDER- GARTNERS. 


Whereas  the  activity  of  the  cutting  itself, 
the  logical  progress  in  it  advances  a  most 
beneficial  influence  upon  the  intellect  of  the 
pupil,  the  results  of  it  will  awaken  his  sense 
of  beauty,  his  taste  for  the  symmetrical,  his 
appreciation  of  harmony  in  no  less  degree. 
The  simplest  cut  already  yields  an  abundance 
of  various  figures.  If  we  make  as  in  Fig.  5,  Plate 
LI.,  two  perpendicular  cuts,  and  unfold  all 
single  parts,  we  shall  have  a  square  with 
hollow  middle,  a  small  square,  and  finally  the 
frame  of  a  square.  If  we  cut  according  to 
Fig  6,  we  produce  a  large  octagon,  four 
small  triangles,  four  strips  of  paper  of  a  trape 
zium  form,  nine  figures  altogether. 

All  these  parts  are  now  symmetrically  ar- 
ranged according  to  the  law :  union  of  op 
posites — here  effected  by  the  position  or  direc- 
tion of  the  parts,  relative  to  the  center — 
and  after  they  have  been  arranged  in  this 
manner,  the  pupils  will  often  express  the  de- 
sire to  preserve  them  in  this  arrangement. 
This  natural  desire  finds  its  gratification  by 

MOUNTING  THE  FIGURES. 
As  separation  always  requires  its  opposite, 
uniting,  so  the  cutting  requires  mounting. 
Plates  LVI.  to  LVIII.  present  some  examples 
from  Which  the  manner  in  which  the  results 
of  the  cutting  may  be  applied,  can  be  easily 
derived.  With  the  simpler  cuts,  the  clippings 
are  to  be  employed,  but  if  a  main  figure  is 


complete  and  in  accordance  with  the  claims 
of  beauty  in  itself,  it  would  be  foolish  to  spoil 
it,  by  adding  the  same. 

This  occupation,  also,  can  be  made  sub- 
servient to  influence  the  intellectual  develop- 
ment of  the  child  by  requiring  it  to  point 
out  all  manners  in  which  these  forms  may 
be  arranged  and  put  together.  (Plate  LVI., 
Fig  5) 

In  order  to  increase  the  interest  of  the  chil- 
dren, to  give  a  larger  scope  to  their  inventive 
power,  and  at  the  same  time,  to  satisfy  their 
taste  and  sense  of  color,  they  may  have  paper 
of  various  colors  and  be  allowed  to  exchange 
their  productions  among  one  another. 

Both  these  occupations,  cutting  and  mount- 
ing, are  for  Kinder  Garten  as  well  as  higher 
grades  of  schools.  For  older  pupils,  the  cut- 
ting out  of  animals,  plants  and  other  forms  of 
life  will  be  of  interest,  and  silhouettes  even 
may  be  prepared  by  the  most  expert. 

It  is  evident  that  not  only  as  a  simple 
means  of  occupation  for  the  children,  during 
their  early  life,  but  as  a  preparation  for  many 
an  occupation  in  real  life,  the  cutting  of  paper 
and  mounting  the  parts  to  figures,  as  intro- 
duced here,  are  of  undeniable  benefit. 

The  main  object,  however,  is  here,  as  in  all 
other  occupations  in  the  Kinder-Garten,  de- 
velopment of  the  sense  of  beauty,  as  a  prep- 
aration for  subsequent  performance  in  and 
enjoyment  of  art. 


THE   FOURTEENTH    GIFT. 


MATERIAL  FOR  BRAIDING  OR  WEAVING. 

(PLATES  LIX.   To   i.XlV.) 


Braiding  Is  a  favorite  occupation  of  chil- 
dren. The  child  instinctively,  as  it  were,  likes 
everything  contributing  to  its  mental  and 
bodily  development,  and  few  occupations  may 


claim  to  accomplish  both,  better  than  the  oc- 
cupation now  introduced  It  requires  great 
care,  but  the  three  year  old  child  may  already 
see  the  result  of  such  care,  whereas  even  from 


GUIDE   TO    KINDER-GARTNERS. 


6i 


twelve  to  fourteen  years  old  pupils  often  have 
to  combine  all  their  ingenuity  and  persever- 
ance to  perform  certain  more  complicated 
tasks  in  the  braiding  or  weaving  department. 
It  does  not  develop  the  right  hand  alone,  the 
left  also  finds  itself  busy  most  of  the  time.  It 
satisfies  the  taste  of  color,  because  to  each 
piece  of  braiding,  strips  of  at  least  two  differ- 
ent colors  belong.  It  excites  the  sense  of 
beauty  because  beautiful,  i.  e ,  symmetrical, 
forms  are  produced  ;  at  least  their  production 
is  the  aim  of  this  occupation.  The  sense  and 
appreciation  of  number  are  constantly  nour- 
ished, nay,  it  may  be  asserted,  that  there  is 
hardly  a  better  means  of  affording  percep- 
tions of  numerical  conditions,  so  thorough, 
founded  on  individual  experience  and  ren- 
dered more  distinct  by  diversity  in  form  and 
color,  than  '■^braiding."  The  products  of  the 
child's  activity,  besides,  are  readily  made  use- 
ful in  practical  life,  affording  thereby  capital 
opportunities  fcr  expression  of  its  love  and 
gratitude,  by  presents  prepared  by  its  own 
hand. 

The  material  used  for  this  occupation  are 
sheets  of  paper  prepared  as  shown  on  Plate 
LIX.,  strips  of  paper,  and  the  braiding  needle, 
also  represented  on  Plate  LIX. 

A  braid  work  is  produced  by  drawing  with 
the  needle  a  loose  strip  (white)  through  the 
strips  of  the  braiding  sheet,  (green)  so  that  a 
number  of  the  latter  will  appear  over,  another 
under  the  loose  strip.  These  numbers  are 
conditioned  by  the  form  the  work  is  to  as- 
sume. As  there  are  but  two  possible  ways 
in  which  to  proceed,  either  lifting  up,  or  pres- 
sing down,  the  strips  of  the  braiding  sheet, 
the  course  to  be  taken  by  the  loose  strip  is 
easily  expressed  in  a  simple  formula.  All 
varieties  of  patterns  are  expressible  in  such 
formulas,  and  therefore  easily  preserved  and 
communicated. 

The  simplest  formula  of  course,  is  when  one 
strip  is  raised  and  the  next  pressed  down. 
We  express  ihis  formula  by  i  u  {up),  i  d 
(down).  All  such  formulas  in  which  only  two 
figures    occur,  are    called    simple    formulas ; 


combination  formulas,  however,  are  such  as 
contain  a  combination  of  two  or  more  such 
simple  formulas. 

But  with  a  single  one  of  such  formulas,  no 
braid  work  can  yet  be  constructed.  If  we 
should,  for  instance,  repeat  with  a  second, 
third,  and  fourth  strip,  i  u,  i  //,  the  loose 
strips  would  slip  over  one  another  at  the 
slightest  handling,  and  the  strips  of  the  braid- 
ing sheet  and  the  whole  work,  drop  to  pieces 
if  we  should  cut  from  it,  the  margin.  In  do- 
ing the  latter,  we  have,  even  with  the  most 
perfect  braid  work,  to  employ  great  care  ;  but 
it  is  only  then  a  braid  or  weaving  work  exists 
— when  all  strips  are  joined  to  the  whole  by 
other  strips,  and  none  remain  entirely  de- 
tached. 

To  produce  a  braid  work,  we  need  at  least 
two  formulas,  which  are  introduced  alternately. 
Proceeding  according  to  the  same  fundamen- 
tal law  which  has  led  us  thus  far  in  all  our 
work,  we  combine  first  with  i  u,  i  d,  its  oppo- 
site I  d,  1  u. 

Such  a  combination  of  braiding  formulas 
by  which  not  merely  a  single  strip,  but  the 
whole  braid  work,  is  governed,  is  a  braidmg 
scheme. 

Braiding  formulas,  according  to  which  the 
single  strip  moves,  are  easily  invented.  Even 
if  one  would  limit  one's  self  to  take  up  or  press 
down  no  more  than  five  strips,  (and  such  a 
limitation  is  necessary,  because  otherwise  the 
braiding  would  become  too  loose,)  the  follow- 
ing thirty  formulas  vyould  be  the  result : 

1,  lu  id  9,  3u  id  17,  411  2d  24,  5d  lu 

2,  id  lu  10,  3d  lu  18,  4d  2u  25,  511  2d 

3,  2u  2d  II,  311  2d  19,  411  3d  26,  5d  2U 

4,  2d  2u  12,  3d  2u  20,  4d  311  27,  511  3d 

5,  211  id  13,  4u  4d  21,  511  5d  28,  5d  3U 

6,  2d  lu  14,  4d  4n  22,  5d  5U  29,  5U  4d 

7,  3u  3d  15,  411  id  23,  5u  id  30,  5d  4U 

8,  3d  311  16,  4d  lu 

From  these  thirty  formulas,  among  which  are 
always  two  oppositionally  alike,  as  for  in- 
stance, I  and  2,  9  and  10,  25  and  26,  hun- 
dreds of  combined,  or  combination  formulas 
can  be  formed  by  simply  uniting  two  of  them. 
In  the  beginning  it  is  advisable  to  combine 


62 


GUIDE  TO   KINDER-GARTNERS. 


such  as  contain  equally  named  numbers  either 
even  or  odd.  The  following  are  some  ex- 
amples : 

Formulas    i    and  3,  lu  id,   2u   2d. 

"  I    and  5,  lu  id,   2u    id. 

"  I    and  7,  lu  id,   311   3d. 

"  I    and  9,  lu  id,    311    id. 

"  I    and  II,  III  id,    3U    2d. 

"  I   and  13,  III  id,   411   4d. 

"  I   and  15,  lu  id,   4U    id. 

"  I    and  ij,  lu  id,   4U   2d. 

"  I    and  19,  lu  id,   411   3d. 

"  I    and  21,  lu  id,   5U   5d. 

"  I    and  23,  lu  id,    5U    id. 

"  I    and  25,  lu  id,   5U   2d. 

"  I    and  27,  lu  id,    5U   3d. 

"  I    and  29,  lu  id,    5U   4d. 

If  we  also  add  the  formulas  under  the  even 
numbers  in  the  given  thirty,  we  have  to  read 
them  inversely.     Thus : 

Formulas    l    and  6,  lu  id,  lu  2d. 

"  I    and  10,  III  id,  lu  3d. 

"  I    and  12,  lu  id,  2u  3d. 

"  I    and  16,  lu  id,  lu  4d. 

"  I    and  18,  lu  id,  2u  4d. 

"  I    and  20,  lu  id,  3U  4d. 

"  I    and  24,  III  id,  lu  5d. 

"  I    and  26,  lu  id,  2u  5d. 

"  I   and  28,  lu  id,  3U  5d. 

*'  I    and  30,  lu  id,  4u  5d. 

By  a  combination  of  one  single  formula 
with  the  twenty  four  others,  we  receive  new 
combination  formulas  and  see  that  inventing 
formulas  is  a  simple  mathematical  operation, 
regulated  by  the  laws  of  combination. 

Much  more  difficult  it  is  to  invent  braidmg 
schemes.  Not  to  dwell  too  long  on  this  point, 
we  introduce  the  reader  to  the  course  shown 
in  pictures  on  our  plates,  which  is  arranged  so 
systematically  that  either  as  a  whole  or  with 
some  omissions,  it  may  be  worked  through 
with  children  from  three*  to  six  years,  as  a 
Jjraiding  school.  It  begins  with  simple  formu- 
las and  by  means  of  the  law  of  opposites  is 
carried  out  to  the  most  beautiful  figures. 

Formula  i,  lu  id,  (Fig.  i,)  is  first  intro- 
duced ;  opposite  in  regard  to  number  is  2U 
2d,  (Fig.  2).  In  Fig.  3  the  numbers  i  and  2 
are  combined ;  Fig.  4  is  a  combination  of 
Figs.  I  and  2 ;  Fig.  5  a  combination  of  Figs. 


I  and  3  by  combining  the  simple  formulas. 
If  we  examine  Fig.  5,  the  number  3  makes 
itself  prominent  in  the  strips  running  ob- 
liquely. In  Fig.  6  it  occurs  independently  as 
opposite  to  I  and  2,  and  then  follows  in  Figs. 
7-15  a  series  of  mediative  forms  all  uniting 
the  opposites  in  regard  to  number.  In  all 
these  patterns  the  squares  or  oblongs  pro- 
duced, are  arranged  perpendicularly  under,  or 
horizontally  beside,  one  another.  Except  in 
Fig.  I,  the  oblique  line  appears  already  be- 
side the  horizontal  and  perpendicular.  Thus, 
this  given  opposite  of  form  is  prevailing  on 
Plate  LXL,  and  we  apply  here  the  same  for- 
mulas as  on  Plate  LX.,  with  the  difference, 
however,  that  we  need  only  one  formula, 
which  in  the  second,  third  strip,  etc.,  always 
begins  one  strip  later  or  earlier.  Thus  in 
Fig.  16,  the  formula  2u  2d  (as  in  Fig.  2)  is 
carried  out.  The  dark  and  light  strips  of  the 
pattern  run  here  from  right  above  to  left  be- 
low. Opposite  of  position  to  Fig.  16,  is 
shown  in  Fig.  17,  where  both  run  the  oppo- 
site way.  Fig.  18  shows  combination,  and 
Fig.  19  double  combination.  In  opposition 
to  the  connected  oblique  lines,  the  broken  line 
appears  in  Fig.  20.  As  the  formula  2u  2d 
has  furnished  us  five  patterns,  so  the  formula 
of  Fig.  3,  lu  2d,  furnishes  the  series  21 — 25. 
Nos.  21  and  22  are  opposites  as  to  direction. 
Fig.  23  shows  the  combination  of  these  op- 
posites. Figs.  24  and  25,  opposites  to  one 
another,  are  forms  of  mediation  between  21 
and  22.  -With  them  for  the  first  time  a  mid- 
dle presents  itself 

While  in  Figs.  21 — 26  the  dark  color  is 
prevailing,  Figs.  26 — 28  show  us  predom- 
inantly, the  light  strip,  consequently  the  op- 
posite in  color.  In  29 — 32,  formulas  from  Figs. 
3 — 5  are  employed.  Fig.  29  requires  an  op- 
posite of  direction,  a  pattern  in  which  the  strips 
run  from  left  above  to  right  below.  Fig.  30 
gives  the  combination  of  both  directions  and 
Figs.  31  and  32  are  at  the  same  time  op- 
posites as  to  direction  and  color. 

It  is  obvious  that  each  single  formula  can 
be  used  for  a  whole  series  of  divers  patterns, 


GUIDE   TO    KINDER-GARTNERS. 


63 


and  the  invention  of  tliese  patterns  is  so  easy 
that  it  will  suffice  if  we  introduce  each  new 
formula  very  briefly. 

Fig.  ;^;i  is  a  form  of  mediation  for  the  for- 
mula 3U  3d  ;  Fig.  34  shows  a  different  appli- 
cation of  the  same  formula.  In  Fig.  35  the 
broken  line  appears  again,  but  in  opposition 
to  20,  it  changes  its  direction  with  each  break. 
In  Figs.  36 — 40  the  formulas  of  Figs.  7,  8, 
10,  II,  and  13  are  carried  out.  The  braiding 
school,  per  se,  is  here  concluded.  Whoever 
may  think  it  too  extensive  may  select  from  it 
Nos.  I.  2,  3  6,  7,  ID,  16,  17,  18,  21,  26,  24, 
25.  33-  and  34 

But  if  any  one  would  like  still  to  enlarge 
upon  it,  she  may  do  so  by  working  out,  for 
each  siugle  formula  the  forms  or  patterns 
16,  17.  18,  19,  24  and  25.  and  continue  the 
school  to  the  number  5.  The  number  of  pat 
terns  will  be  made,  thereby,  ten  times  larger. 

Another  change,  and  enlargement  of  the 
school  may  be  introduced  by  cutting  the 
braiding  strips,  as  well  as  those  of  the  braiding 
sheet,  of  different  widths.  We  can,  thereby, 
represent  quite  a  number  of  patterns  after 
the  same  formula,  which  are,  however,  essen- 
tially different.  This  is  particularly  to  be 
recommended  with  very  small  children,  who 
necessarily  will  have  to  be  occupied  longer 
with  the  simple  formula  lu  id.  But  for  more 
developed  braiders,  such  change  is  of  interest, 
because  by  it  a  great  variety  of  forms  may 
be  produced  which  may  be  rendered  still 
more  interesting  and  attractive,  by  a  variety 
of  colors  in  the  loose  braiding  strips. 

With  patterns  that  have  a  middle,  as  24 
and  28,  it  is  advisable  to  let  the  braiding  be- 
gin (especially  with  beginners,)  with  the  mid- 
dle strip,  and  then  to  insert  always  one  strip 
above,  and  one  below  it 


It  is  not  unavoidably  necessary  that  the 
school  should  be  finished  from  beginning  to 
end,  as  given  here.  Quite  the  reverse  The 
pupil,  after  having  successfully  produced  some 
patterns,  may  be  afforded  an  opportunity  for 
developing  his  skill  by  his  own  invention,  in 
trying  to  form,  by  braiding  a  cross,  with  hol- 
low middle,  (Fig.  41,)  a  standing  oblong.  (42,) 
a  long  cross,  (43,)  a  small  window,  (45,)  etc. 

Plate  LXIII  ,  presents  some  patterns  which 
may  be  used  for  wall  baskets,  lamp  tidies, 
book-marks,  etc.,  and  which  may  easily  be 
augmented  by  such  as  have  acquired  more 
than  ordinary  skill. 

Finally,  Plate  LXIV.  shows  in  figures  i — 3, 
obliquely  intertwined  strips,  representing  the 
so  called  free  braiding,  the  braiding  without 
braiding  sheet.  This  is  done  in  the  following 
manner  :  Cut  two  or  more  long  strips  (Fig.  4) 
of  a  quarter  sheet  of  colored  paper,  (green,) 
and  fold  to  half  their  length,  (Fig.  5,)  cut 
then,  of  differently  colored  paper,  (white,) 
shorter  strips,  afso  fold  these  to  half  their 
length.  Put  the  green  strips  side  by  side  of 
one  another,  as  shown  in  Fig.  7,  so  that  the 
closed  end  of  the  one  strip  lies  above,  and 
that  of  the  other  below,  (jcc.)  Then  take 
the  white  strip,  bend  it  around  strip  i,  and 
lead  it  through  strip  2,  (Fig  8.)  The  second 
strip  is  applied  in  an  opposite  way,  laying  it 
around  2,  and  leading  it  throu£:h  i.  Em- 
ploying four  instead  of  two  green  strips,  the 
book  mark.  Fig.  9,  will  be  the  result.  The 
protruding  ends  are  either  cut  or  scolloped. 
By  introducing  strips  of  different  widths, 
a  variety  of  patterns  can  fi iso  here  be  pro- 
duced. 

Instead  of  paper,  glaztd  muslin,  leather, 
silk  or  woolen  ribbon,  strav/  aud  the  like  may 
be  used  as  material  for  hvudi'r/^ 


THE    FIFTEENTH   GIFT. 


THE   INTERLACING   SLATS. 


(plates  lxv.  and  IXVI.) 


Froebel,  in  his  Gifts  of  the  Kinder-Garten, 
does  not  present  anything  perfectly  new.  All 
his  means  of  occupation  are  the  result  of  care- 
ful observation  of  the  playing  child.  But  he 
has  united  them  in  one  corresponding  whole; 
he  has  invented  a  method,  and  by  this  method 
presented  the  possibility  of  producing  an  ex- 
haustless  treasure  of  formations  which,  each 
influencing  the  mind  of  the  pupil  in  its  pecu- 
liar way,  effect  a  development  most  harmoni- 
ous and  thorough  of  all  the  mental  faculties. 
The  use  of  slats  for  interlacing  is  an  occupa- 
tion already  known  to  our  ancestors,  and  who 
has  not  practiced  it  to  some  extent  in  the 
days  of  childhood  ?  But  who  has  ever  suc- 
ceeded in  producing  more  than  five  or  six 
figures  with  them  ?  Who  has  ever  derived, 
from  such  occupation,  the  least  degree  of  that 
manual  dexterity  and  mental  development, 
inventive  power  and  talent  of  combination, 
which  it  affords  the  pupils  of  the  Kinder  Gar- 
ten, since  Froebel 's  method  has  been  applied 
to  the  material  ? 

Our  slats,  ten  inches  long,  three-eighths  of 
an  inch  broad  and  one-sixteenth  of  an  inch 
thick,  are  made  of  birch  or  any  tough  wood, 
and  a  dozen  of  them  are  sufficient  to  produce 
quite  a  variety  of  figures.  They  form,  as  it 
were  the  transition  from  the  plane  of  the  tab- 
let to  the  line  of  the  staffs.  (Ninth  Gift)  differ- 
ing, however,  from  both,  in  the  fact  that  forms 
produced  by  them  are  not  bound  to  the  plane, 
but  contain  in  themselves  a  sufficient  hold  to 
be  separated  from  it. 

The  child  first  receives  one  single  slat.     Ex- 


amining it,  it  perceives  that  it  is  flexible,  that 
its  length  surpasses  its  breadth  many  times, 
and  again  that  its  thickness  is  many  times 
less  than  its  breadth. 

Can  the  pupil  name  some  objects  between 
which  and  the  slat,  there  is  any  similarity .'' 

The  rafters  under  the  roof  of  a  house,  and 
in  the  arms  of  a  wind-mill,  and  the  laths  of 
which  fences,  and  certain  kinds  of  gates,  and 
lattice  work  are  made,  are  similar  to  the  slat. 

The  child  ascertains  that  the  slat  has  two 
long  plane  sides  and  two  ends.  It  finds  its 
middle  or  center  point,  can  indicate  the  upper 
and  lower  side  of  the  slat,  its  upper  and  lower 
end,  and  its  right  and  left  side.  After  these 
preliminaries,  a  second  slat  is  given  the  child. 
On  comparison  the  child  finds  them  perfectly 
alike,  and  it  is  then  led  to  find  the  positions 
which  the  two  slats  may  occupy  to  each  other. 
They  can  be  laid  parallel  with  each  other,  so 
as  to  touch  one  another  with  the  whole  length 
of  their  sides,  or  they  may  not  touch  at  all. 

They  can  be  placed  in  such  positions  that 
their  ends  touch  in  various  ways,  and  can  be 
laid  crosswise,  ov-er  or  under  one  another. 

With  an  additional  slat,  the  child  now  con- 
tinues these  experiments.  It  can  lay  various 
figures  with  them,  but  there  is  no  binding  or 
connecting  hold.  Therefore  as  soon  as  it  at- 
tempts to  lift  its  work  from  the  table,  it  falls 
to  pieces. 

By  the  use  o^fotir  slats,  it  becomes  enabled 
to  produce  something  of  a  connected  whole, 
but  this  only  is  done,  when  each  single  slat 
C0J71CS  in  contact  with  at  least  three  other  slats. 


GUIDE    TO    KINDER-GARTNERS. 


Two  of  these  should  be  on  one  side,  the  third 
or  middle  one  should  rest  on  the  other  side 
of  the  connecting  slat,  so  that  here  again  the 
law  of  opposites  and  their  mediation  is  fol- 
lowed and  practically  demonstrated  in  every 
figure. 

It  is  not  easy  to  apply  this  iaw  constantly 
in  the  most  appropriate  manner.  But  this 
very  necessity  of  painstaking,  and  the  reason- 
ing, without  which  little  success  will  be  at- 
tained, is  productive  of  rich  fruit  in  the  de- 
velopment of  the  pupil. 

The  child  now  places  the  slat  aa  horizon  • 
tally  upon  the  table.  Bb  is  placed  across  it 
in  a  perpendicular  direction  ;  cc  xxs.  2,  slanting 
direction  under  a  and  b,  and  dd  is  shoved  under 
aa  and  over  bb  and  under  cc,  as  shown  in  Fig.  i. 

This  gives  a  connected  form,  which  will  not 
easily  drop  apart.  The  child  investigates 
how  each  single  slat  is  held  and  supported — 
it  indicates  the  angles,  which  were  created, 
and  the  figures  which  are  bounded  by  the  va- 
rious parts  of  the  slats. 

To  show  how  rich  and  manifold  the  material 
for  observation  and  instruction  given  in  this 
one  figure  is,  we  will  mention  that  it  contains 
twenty-four  angles,  of  which  8  (i — 8)  are 
right,  8  (9 — 16)  acute,  and  8  {17 — 24)  obtuse 
— formed  by  one  perpendicular  slat,  bb,  one 
horizontal,  aa,  one  slanting  from  left  above 
to  right  below,  cc,  and  another  slanting  from 
right  above  to  left  below,  dd. 

Each  single  slat  touches  each  other  slat 
once;  two  of  them,  aa  and  bb  pass  over  two 
and  under  one  and  the  others,  cczx\^  dd,  pass 
under  two  and  over  one  of  the  other  slats,  by 
which  interlacing,  three  small  figures  are 
formed  within  the  large  figure,  one  of  which 
is  a  figure  with  two  right  one  obtuse  and  one 
acute  angle,  (3,  6,  22,  10),  and  four  unequal 
sides,  and  two  others,  one  of  which  is  a  right 
angled  triangle  with  two  equal  sides,  and  the 
other  is  a  right  angled  triangle  with  no  equal 
sides. 

By  drawing  the  slats  of  Fig.  i  apart,  Fig. 
2,  an  acute  angled  triangle  is  produced— by 
drawing  them  together.  Fig.  3  results,  from 


which  the  acute  angled  triangle  Fig.  4,  can 
again  be  easily  formed.  Each  of  these  fig- 
ures presents  abundant  matter  for  investiga- 
tion and  instructive  conversation,  as  shown 
above  in  connection  with  Fig.  i. 

The  child  now  receives  2i  fifth  slat.  Sup- 
pose we  have  Fig.  2,  consisting  of  four  slats 
— ready  before  us — we  can,  by  adding  the 
fifth  slat,  easily  produce  what  appears  on 
Plate  LXV.  as  Fig.  8. 

If  the  five  slats  are  disconnected,  the  child 
may  lay  two,  perpendicularly  at  some  distance 
from  each  other,  a  third  in  a  slanting  position 
over  them  from  right  above  to  left  below,  and 
a  fourth  in  an  opposite  direction,  when  the 
two  latter  will  cross  each  other  in  their  mid 
die.  By  means  of  the  fifth  slat  the  interlac- 
ing then  is  carried  out.  by  sliding  it  from 
right  to  left  under  the  perpendicular  over  the 
crossing  two.  and  again  under  the  other  perpen- 
dicular slat,  and  thereby  the  figure  5  made  firm. 

By  bending  the  perpendicular  slats  together, 
Fig.  6  is  produced;  when  the  horizontal  slat 
assumes  a  higher  position,  a  five  angled  fig- 
ure appears — one  of  the  slanting  slats,  how- 
ever, has  to  change  its  position  also,  as  shown 
in  Fig.  7.  In  Fig.  8,  the  horizontal  slat  is 
moved  downward.  In  Fig.  9,  the  original 
position  of  the  crossing  slats  is  changed ;  in 
the -triangle,  Fig.  10,  still  more,  and  in  Figs. 
II  and  12,  other  changes  of  these  slats  are 
introduced. 

The  addition  of  a  sixth  slat  enables  us  still 
further  to  form  other  figures  from  the  previous 
ones — Fig.  17  can  be  produced  from  9,  18 
from  10  or  11,  22  from  12,  and  then  a  fol- 
lowing series  can  be  obtained  by  drawing 
apait  and  shoving  together  as  heretofore. 

Let  us  begin  thus  :  the  child  lays  (Fig  13) 
two  slats  horizontally  upon  the  table — two 
slats  perpendicularly  over  them ;  a  large 
square  is  produced.  A  fifth  slat  horizontally 
across  the  middle  of  the  two  perpendicular 
slats,  gives  two  parallelograms,  and  by  con- 
necting the  sixth  slat  from  above  to  below  with 
the  three  horizontal  slats  so  that  the  middle 
one  is  under  and  the  two  outside  slats  over  it, 


66 


GUIDE    TO    KINDER  GARTNERS. 


the  child  will  have  formed  four  small  squares, 
of  equal  size 

The  figures  17  and  i8,  (triangles.)  and  19 
and  23,  (hexagons,)  deserve  particular  atten- 
tion, because-  they  afford  valuable  means  for 
mathematical  observations. 

On  Plate  LXVI.  we  find  some  few  ex- 
amples of  seven  intertwined  slats,  (Figs.  25 — 
28,)  of  eight  slats,  (Figs.  29 — t,6,)  of  nine  slats, 
(Figs.  37 — 40,)  and  often  slats.  (Figs  41 — 43.) 

All  we  have  given  in  the  above  are  mere 
hints  to  enable  the  teacher  and  pupil  to  find 
more  readily  by  individual  application,  the 
richness  of  figures  to  be  formed  with  this  oc- 
cupation material. 

It  is  particularly  mathematical  forms,  reg- 
ular polygons,  (Figs.  28,  31,  40,  42,)  contem- 
plation of  divisions,  produced  by  diagonals, 
etc.,  planes  and  proportions  of  form,  which, 
m  forms  of  knowledge^  are  brought  before  the 
eye  of  the  pupil,  with  great  clearness  and  dis- 
tinctness, by  the  interlacing  slats. 

In  the  meantime,  it  will  afford  pleasure  to 
behold  the  fonns  of  beauty,  as  given  in  Figs. 
3o>  ZZ^  37 ;  nor  should  the  forms  of  life  be 
forgotten,  as  they  are  easily  produced  by  a 
larger  number  of  slats,  (Fig.  39 — a  fan  ;  35 
and  36 — fences,)  by  combining  the  work  of 
several  pupils. 


The  figures  are  not  simply  to  be  constructed 
and  to  be  changed  to  others,  but  each  of  them 
is  to  be  submitted  to  a  careful  investigation 
by  the  child,  as  to  its  angles,  its  constituent 
parts,  and  their  qualities,  and  the  service  each 
individual  slat  performs  in  the  figure  as  indi- 
cated with  Fig.  I ,  on  page  LXV. 

The  occupation  with,  this  material  will  fre- 
quently prove  perplexing  and  troublesome 
to  the  pupil  ;  oftentimes  he  will  try  in  vain 
to  represent  the  object  in  his  mind. 

Having  almost  successfully  accomplished 
the  task,  one  of  the  slats  will  glide  out  from 
his  structure,  and  the  whole  will  be  a  mass 
of  ruins  It  was  the  one  slat,  which,  owing  to 
its  dereliction  in  performing  its  duty,  des 
troyed  the  figure,  and  prevented  all  the  others 
from  performing  theirs. 

It  will  not  be  difficult  for  the  thinking 
teacher  to  derive  from  such  an  occurrence, 
the  opportunity  to  make  an  application  to 
other  conditions  in  life,  even  within  the  sphere 
of  the  young  child,  and  its  companions  in  and 
out  of  school.  The  character  of  this  occu- 
pation does  not  admit  of  its  introduction  be- 
fore the  pupils  have  spent  a  considerable  time 
in  the  Kinder  Garten,  in  which  it  is  only  be- 
gun, and  continued  in  the  primary  depart- 
ment. 


THE  SIXTEENTH  GIFT. 


THE    SLAT    WITH    MANY    LINKS. 


This  occupation  material,  which  may  be 
used  at  almost  any  grade  of  development  in 
the  Kinder  Garten,  the  primary  and  higher 
school  departments,  is  so  rich  in  "its  applica- 
tions, that  we  cannot  attempt  to  describe  it 
extensively,  nor  give  illustrations  of  the  vari- 
ous ways  in  which  it  can  be  rendered  useful. 
Suffice  it  to  say,  that  it  may  be  employed  in 
representing  all  various  kinds  of  lines,  angles 


and  mathematical  figures,  and  that  even  forms 
of  life  and  beauty  may  be  presented  by  it. 

We  have  slats  with  4,  6,  8  and  16  links, 
which  are  introduced  one  after  the  other  when 
opportunities  offer.  In  placing  the  first  into 
the  hand  of  the  child,  we  would  ask  him  to 
unfold  all  the  links  of  the  slat,  and  to  place 
it  upon  the  table  so  as  to  represent  a  perpen- 
dicular, horizontal,  and  then  an  oblique  line. 


GUIDE   TO    KINDER-GARTNERS. 


67 


By  bending  two  of  the  Ihiks  perpendicularly, 
and  the  two  others  horizontally,  we  form  a 
right  angle.  Bending  one  of  the  legs  of  the 
angle  toward,  or  from  the  other,  we  receive 
the  acute  and  obtuse  angles,  which  grow 
smallpr  or  larger,  the  nearer  or  •  farther  the 
legs  are  brought  to,  or  from  each  other,  until 
we  reduce  the  angles  to  either  a  perpendicular 
line  of  two  links'  length,  or  a  horizontal  line 
of  the  length  of  four  links. 

We  may  then  form  a  square.  Pushing  two 
opposite  corners  of  it  toward  each  other,  and 
bending  the  first  link  so  as  to  cover  with 
it  the  second,  and,  by  then  joining  the 
end  of  the  fourth  link  to  where  the  first 
and  second  are  united,  we  shall  form  an 
equilateral  triangle.  (Which  other  triangle 
can  be  formed  with   this  slat,  and  how  ?) 

The  capital  letters  V,  W,  N,  M,  Z,  and  the 
figure  4  can  be  easily  produced  by  the  chil- 
dren, and  many  figures  be  constructed  by  the 
teacher  in  which  the  pupils  may  designate  the 


number  and  kinds  of  angles,  which  they  con- 
tain, as  is  done  with  the  movable  slats  on 
other  occasions. 

The  slats  with  6.  8  and  16  links,  to  be 
introduced  one  after  the  other,  if  used 
in  the  manner  here  indicated,  can  be  ren- 
dered exceedingly  interesting  and  instruct- 
ive to  the  pupils.  Their  ingenuity  and  in- 
ventive power  will  find  a  large  field  in  the 
occupation  with  this  material  if,  at  times, 
they  are  allowed  to  produce  figures  them- 
selves, of  which  the  more  advanced  pupils 
may  make  drawings  and  give  a  description 
of  each  orally. 

It  would  be  needless  to  enlarge  here  upon 
the  richness  of  material  afforded  by  this  gift, 
as  half  an  hour's  study  of  and  practice  with  it 
will  convince  eath  thinking  teacher  fully  of 
the  treasure  in  her  hand  and  certainly  make 
her  admire  it  on  account  of  the  simplicity  of 
its  application  for  educational  purposes  in 
school  and  family. 


THE   SEVENTEENTH    GIFT. 


MATERIAL  FOR  INTERTWINING. 

(plates   LXVIl.,    LXVIII.) 


Intertwining  is  an  occupation  similar  to 
that  of  interlacing.  Aim  of  both  is  repre- 
sentation of  plane — outlines.  In  the  occupa- 
tion with  the  interlacing  slats  we  produced 
forms,  which  were  to  be  destroyed  again,  or 
whose  peculiarities,  at  least,  had  to  be  changed 
to  produce  something  new ;  here,  we  produce 
permanent  results.  There,  the  material  was 
in  every  respect  a  ready  one;  here,  the  pupil 
has  to  prepare  it  himself.  There,  hard  slats 
of  little  flexibility  ;  here,  soft  paper,  easily 
changed.  There,  production  of  purely  math- 
ematical forms  by  carefully  employing  a  given 
material;   here,  production  of  similar  forms 


by  changing  the  material,  which  forms,  how- 
ever, are  forms  of  beauty. 

The  paper  strips,  not  .used  when  preparing 
the  folding-sheets,  are  used  as  material,  adapted 
for  the  present  occupation.  They  are  strips 
of  white  or  colored  paper,  from  eight  to  ten 
inches  long  and  varying  in  breadth.  Each 
strip  is  subdivided  in  smaller  strips  of  three- 
quarters  of  an  inch  wide,  which  by  folding 
their  long  sides  are  transformed  to  threefold 
strips  of  eight  to  ten  inches  long  and  one- 
quarter  of  an  inch  wide. 

The  children  will  not  succeed  well,  in  form  " 
ing  regular  figures  from  these  strips  at  first.  1^ 


68 


GUIDE   TO    KINDER-GARTNERS. 


As  the  main  object  of  this  occupation  is  to 
accustom  the  child  to  a  clean,  neat  and  cor- 
rect performance  of  his  task,  some  of  the 
tablets  of  Gift  Seven  are  given  him  as  pat- 
terns to  assist  him  ;  or  the  child  is  led  to  draw 
on  his  slate  the  three,  four,  or  many  cornered 
forms,  and  to  intertwine  his  paper  strips  ac- 
cording to  these. 

Eirst,  a  right  angled  isosceles  triangle  is  used 
for  laying  around  it  one  of  these  strips  so  as 
to  enclose  it  entirely.  We  begin  with  the  left 
cathetus,  put  the  tablet  upon  the  strip,  folding 
it  toward  the  right  over  the  right  angle.  The 
break  of  the  paper  is  well  to  be  pressed  down, 
and  then  the  strip  is  again  folded  around  the 
acute  angle  toward  the  left.  Where  the  hy- 
potenuse (large  side)  touches  the  left  cathetus 
(small  side),  the  strip  is  cut  and  the  ends  of 
the  figure  there  closed  by  gluing  them  to- 
gether by  some  clean  adhesive  matter.  Care 
should  be  taken  tliat  the  one  end  of  each  side 
be  under,  the  other  over,   that  of  the  other. 

Thus  the  various  kinds  of  triangles,  (Figs. 
I — 3,)  squares,  rhombus,  rhomboids,  etc.,  are 
produced. 

Two  like  figures  are  combined,  as  shown  in 
Figs.  4 — 6.  If  strips  prove  to  be  too  short, 
the  child  is  shown  how  to  glue  them  together, 
to  procure  material  for  larger  and  more  com- 
plicated forms.  Thus,  it  produces,  with  one 
long  strip.  Figs.  i6,  i8,  19,  20;  with  two  long 
strips.  Figs.  17,  21.  Fig.  22  shows  the  natu- 
ral size  ;  all  others  are  drawn  on  a  somewhat 
reduced  scale.  It  cannot  be  difficult  to  pro- 
duce a  great  variety  of  similar  figures,  if  one 
will  act  according  to  the  motives  obtained  with 
and  derived  from  the  occupation  with  the  in- 
terlacing slats. 


This  occupation  admits  of  still  another  and 
very  beautiful  modification,  by  not  only  pinch- 
ing and  pressing  the  strip  where  it  forms 
angles,  but  by  folding  it  to  a  rosette.  This 
process  is  illustrated  in  Figs.  7 — 9.  The  strip 
is  first  pinched  toward  the  right,  (Fig.  7,)  then 
follows  the  second  pinch  downward,  (Fig  8,) 
then  a  third  toward  the  left,  when  the  one  end 
of  the  strip  is  pushed  through  under  the  other, 

(Fig  9-) 

Here,  also,  simple  triangles,  squares,  pen- 
tagons and  hexagons  are  to  be  formed,  then 
two  like  figures  combined,  and  finally  more 
complicated  figures  produced.  (Compare  ex- 
amples given  in  Figs    10 — 15.) 

Whatever  issues  from  the  child's  hand  suffi- 
ciently neat  and  clean  and  carefully  wrought, 
may  be  mounted  on  stiff  paper  or  bristol 
board,  and  disposed  of  in  many  ways. 

The  occupation  of  intertwining  shows 
plainly  how  by  combination  of  simple  mathe- 
matical forms,  forms  of  beauty  may  be  pro- 
duced. These  latter  should  predominate  in 
the  Kinder-Garten,  and  the  mathematical  arc 
of  importance  as  they  present  the  elements  for 
tlieir  construction.  The  mathematical  ele 
nient  of  all  our  occupations  is  in  so  far  of 
significance,  as  the  child  receives  from  it 
impressions  of  form ;  but  of  much  more  im- 
portance is  the  development  of  the  child's 
taste  for  the  beautiful,  because  with  it,  the 
idea  of  the  good  is  developed  in  the  mean- 
time. 

As  the  various  performances  of  this  occu- 
pation, cutting,  folding  and  mounting,  require 
a  somewhat  skilled  hand,  it  is  introduced 
in  the  upper  section  of  the  Kinder  Garten 
only. 


THE   EIGHTEENTH    GIFT. 


MATERIAL  FOR  PAPER -FOLDING. 
(plates  lxix.  to  lxxi.) 


Froebel's  sheet  of  paper  for  folding,  the 
simplest  and  cheapest  of  all  materials  of  oc- 
cupation, contains  within  it  a  great  multitude 
of  instructive  and  interesting  forms.  Almost 
every  feature  of  mathematical  perceptions,  ob- 
tained by  means  of  previous  occupations,  we 
again  find  in  the  occupation  of  paper-folding. 
It  is  indeed  a  compendium  of  elementary 
mathematics,  and  has,  therefore,  very  justly 
and  judiciously  been  recommended  as  a  use- 
ful help  in  the  teaching  of  this  science  in 
public  schools. 

Lines,  angles,  figures,  and  forms  of  all 
varieties  appear  before  us,  after  a  few  mo 
ments'  occupation  with  this  material.  The 
multitude  of  impressions,  however,  should 
not  misguide  us  ;  and  we  should  always,  and 
more  particularly  in  this  work,  be  careful  to 
accompany  the  work  of  the  children  with  nec- 
essary conversation  and  pleasant  entertain- 
ment, for  the  relief  of  their  young  minds. 

We  prepare  the  paper  lor  folding  in  the  fol- 
lowing manner : 

Take  half  a  sheet  of  letter  paper,  place  it 
upon  the  table  in  such  a  manner  as  to  have 
the  longest  sides  extend  from  left  to  right. 
Then  halve  it  by  covering  the  upper  corners 
with  the  lower  ones,  (Fig.  i.)  Then  turn  the 
now  left  and  right  upper  (previously  lower) 
corners  back,  towards  the  center ;  invert  the 
paper ;  turn  also  the  two  other  corners  toward 
the  center,  and  then  we  have  the  form  of  a 
trapezium,  (Fig.  2.)  Unfolding  the  sheet  at 
its  base  fine,  a  hexagon,  (Fig.  3.)  will  show 
itself,  in  which  we  observe  four  triangles,  of 


which  two  and  two  lie  together,  forming  a 
larger  triangle.  At  the  base  lines  of  these 
larger  triangles,  the  sheet  is  again  folded,  and 
neatly  and  accurately  cut,  severing  thereby 
the  two  large  double,  lying  triangles  from  the 
single  and  oblong  strips  of  paper. 

Each  of  these  triangles  we  cut  through 
from  where  the  sides  of  the  small  triangles 
touch  each  other,  unfold  the  small  triangles, 
and  we  now  have  four  square  pieces,  and  one 
oblong  piece  of  paper,  (Fig.  4.)  The  former 
we  employ  for  folding,  the  latter  we  keep  for 
future  use,  in  the  occupations  of  intertwining, 
braiding,  or  weaving. 

The  child  should  be  accustomed  to  the 
strictest  care  and  cleanliness  in  the  cutting  as 
well  as  the  folding. 

This  is  necessary,  because  paper  carelessly 
folded  and  cut,  will  not  only  render  more 
difficult  every  following  task,  nay,  make  im- 
possible every  satisfactory  result ;  especially, 
should  this  be  the  case,  because,  we  do 
not  intend  simply  to  while  away  our  own 
and  the  child's  precious  time,  but  are  en- 
gaged in  an  occupation  whose  final  aim  is 
acquisition  of  ability  to  work,  and  to  work 
well — one  of  the  most  important  claims 
human  society  is  entitled  to  make  upon  each 
individual. 

The  child  prepares  for  himself,  in  the  man- 
ner described,  a  number  of  folding  sheets, 
and  submits  them  to  a  series  of  regular 
changes,  by  bending  and  folding,  in  conse- 
quence of  which  the  fundamental  forms  are 
produced,  from  which   sequels   of  forms    of 


70 


GUIDE  TO   KINDER  GARTNERS. 


life  and  beauty  are  subseqently  developed, 
by  means  of  the  law  of  dpposites. 

On  the  road  to  this  goal,  a  surprising  num- 
ber of  forms  of  knowledge  present  them- 
selves. 

The  sheet  is  now  folded  once  more,  fol- 
lowing the  diagonal,  (Fig.  5,)  and  will  then 
present,  when  unfolded,  the  division  of  the 
square,  in  two  right  angled  isosceles  triangles. 

Folded  once  more  according  to  the  other 
diagonal,  (Fig.  6,)  and  again  unfolded,  we  find 
each  of  the  large  triangles,  halved  by  a  per- 
pendicular, (Fig.  7.)  Now  the  lower  corner 
is  bent  upon  the  left,  and  the  right  one  upon 
the  upper,  and  the  sheet  is  so  folded,  that  it 
is  divided  into  equal  oblong  halves  by  a 
transversal.  The  same  is  done  to  the  op- 
posite transversal,  and  we  have  the  Fig.  9, 
affording  a  multitude  of  mathematical  object 
perceptions. 

If  we  now  take  the  lower  corner,  (Fig.  9.) 
bend  it  exactly  toward  the  center  of  the  sheet 
and  fold  it,  the  pentagon,  (Fig.  10.)  will  be  the 
result.  We  fold  the  opposite  corner  in  like 
manner  and  produce  the  hexagon,  (Fig.  11.) 
and  finally  with  the  two  remaining  corners. 
Fig.  12*  is  formed  containing  four  triangles, 
touching  one  another  with  their  free  sides, 
each  of  them  again  showing  a  line  halving 
them  in  two  equal  triangles. 

If  we  invert  12",  we  have  12'',  a  connected 
square,  in  which  the  outlines  of  eight  congru- 
ent triangles  appear.  If  12"  is  unfolded  we 
shall  see  beside  a  multiplication  of  previous 
forms,  parallelograms  also.  If  we  start  from 
12%  fold  the  corners  toward  the  middle,  (Fig. 
15,)  we  shall  receive  a  form  consisting  of 
double  layers  of  paper,  and  showing  four  tri- 
angles, under  which  again,  four  separate 
squares  are  found.  This  is  the  fundamental 
form  for  a  series  of  forms  of  life.  (Fig.  16.) 

It  is  utterly  impossible  to  give  a  minute  de- 
scription how  forms  of  life  may  be  produced 
from  this  fundamental  form.  Practical  at- 
tempts and  occasional  observation  in  the 
Kinder-Garten  will  be  of  more  assistance  than 
the  most  detailed    illustrations    and  descrip- 


tions. Froebel's  Manual  mentions,  among 
others,  the  following  objects :  A  table-clolii 
with  four  hanging  corners,  a  bird,  a  sail  boat, 
a  double  canoe,  a  salt  cellar,  flower,  chemise, 
kite,  wind-mill,  t>>ble,  cigar  holder,  flower- pot, 
looking  glass,  bo.it  with  seats,  etc.  Still  richer 
become  the  forms  of  life,  if  we  bend  the  cor- 
ners of  the  described  fundamental  form,  once 
more  toward  the  middle.  In  connection  with 
.this,  the  manual  mentions  the  following  forms  : 
the  knitting-pouch,  the  chest  of  drawers,  the 
boots,  the  hat,  the  cross,  the  pantaloons,  the 
frame,  the  gondola,  etc.  F"or  the  construction 
of  these  forms,  it  is  advisable  to  use  a  larger 
sheet  of  paper,  perhaps  half  a  sheet  of  letter 
paper. 

But  the  simple  fundamental  form,  for  the 
forms  of  life,  is  also  the  fundamental  form  for 
the  forms  of  beauty,  contained  on  Plate  LXX., 
(Fig.  16.)  Unfold  the  fundamental  form,  do 
not  press  the  corners  but  first  the  middle  of 
the  upper  and  lower  side,  then  the  two  other 
sides  toward  the  middle  of  the  sheet,  and  the 
double  canoe  will  be  the  result  (hexagon  with 
two  long  and  four  short  sides.)  If  the  over- 
reaching triangles  are  now  bent  back  toward 
the  middle.  Fig.  17  appears,  from  which,  up 
to  Fig.  21.  the  following  forms  are  easily  con- 
structed according  to  the  law  of  opposites. 

From  quite  a  similar  fundamental  form,  the 
series  22 — 27  originates. 

If  we  finally  take  the  sheet  as  represented, 
in  12*^  fold  the  lower  right  corner  toward  the 
middle,  also  the  left  upper,  (Fig  13,)  also  the 
two  remaining  corners,  we  shall  have  four 
triangles,  consisting  of  a  double  layer  of  pa 
per  which  may  be  lifted  up  from  the  square 
ground  and  which  upper  layer  again  is- divi- 
ded in  two  triangles,  (Fig.  14  ) 

Invert  this  figure  and  you  will  have  Fig.  28. 
four  single  squares,  the  fundamental  form  of 
a  series  of  forms  of  beauty  on  Plate  LXXI.  ; 
the  latter  easily  to  be  derived  from  this  former, 
under  the  guidance  of  the  well  known  law  of 
opposites. 

The  hints  given  in  the  above  might  be  aug- 
mented to  a  considerable  extent  and  still  not 


GUIDE   TO    KLXDEk-GARTNERS. 


71 


exhaust  the  matter.  They  are  given  espe- 
cially to  stimulate  teacher  and  child  to  indi- 
vidual practical  attempts  in  producing  forms 
by  folding.  The  best  results  of  their  activity 
can  be  improved  by  cutting  out  or  coloring, 
which  adds  a  new  and  interesting  change  to 
this  occupation.  A  change  of  the  fundamental 
form  in  three  directions  yields  various  series 
of  forms  of  beauty,  which  may  be  multi- 
plied ad  infinitum.  Thereby,  not  only  the  idea 
of  sequel  in  representations  is  given,  but  also 
the  understanding  unlocked  for  the  various 
orders  in  nature. 

Furthermore^  this  occupation  gives  the  pu- 


pil such  manual  dexterity  as  scarcely  any 
other  does,  and  prepares  the  way  to  various 
female  occupations,  besides  being  immediately 
preparatory  to  all  plastic  work.  Early  training 
in  cleanliness  and  care  is  also  one  of  the  re 
suits  of  a  protracted  use  of  the  folding  sheet. 
It  is  evident  that  only  those  children  who 
have  been  a  good  while  in  the  KinderGarten, 
can  be  employed  in  this  department  of  occu- 
pation. The  peculiar  fitness  of  the  folding 
sheet  for  mathematical  instruction  beyond  the 
Kinder-Garten,  must  be  apparent  after  we 
have  shown  how  useful  it  can  be  made  in  this 
institiKion. 


THE    NINETEENTH    GIFT. 


MATERIAL  FOR  PEAS  WORK. 

(plates  lxxii.  and  lxxiii.) 


We  have  already  tried,  in  connection  with 
the  Ninth  Gift,  (the  laying  staffs,)  to  render 
permanent  the  productions  of  the  pupils,  by 
stitching  or  pasting  them  to  stiff  paper.  We 
satisfied,  by  so  doing  a  desire  of  the  child, 
which  grows  stronger,  as  the  child  grows 
older — the  desire  to  produce  by  his  own  activ- 
ity certain  lasting  results.  It  is  no  longer  the 
incipient  instinct  of  activity  which  governs  . 
the  child,  the  instinct  which  prompted  it,  ap- 
parently without  aim,  to  destroy  everything 
and  to  reconstruct  in  order  to  again  de- 
stroy. A  higher  pleasure  of  production  has 
taken  its  place  ;  not  satisfied  by  mere  doing, 
but  requiring  for  its  satisfaction  ^Iso  delight 
in  the  created  object — if  even  unconsciously — 
the  delight  of  progress,  which  manifests  itself 
in  the  production,  and  which  can  be  observed 
only  in  and  by  the  permanency  of  the  object 
which  enables  us  to  compare  it  with  objects 
previously  produced. 

To  satisfy  the  claims  of  the  pupil  in  this 


direction  in  a  high  degree,  the  working  with 
peas  is  eminently  fitted,  although  considerable 
manual  skill  is  required  for  it,  not  to  be  ex- 
pected in  any  child  before  the  fifth  year.  The 
material  consists  of  pieces  of  wire  of  the  thick- 
ness of  a  hair-pin,  of  various  sizes  in  length, 
and  pointed  at  the  ends.  They  again  represent 
lines.  As  means  of  combination,  as  embodied 
points  of  junction,  peas  are  used,  soaked  about 
twelve  hours  in  water  and  dried  one  hour  pre- 
vious to  being  used  They  are  then  just  soft 
enough  to  allow  the  child  to  introduce  the 
points  of  the  wires  into  them  and  also  hard 
enough  to  afford  a  sufficient  hold  to  the  latter. 

The  first  exercise  is  to  combine  two  wires, 
by  means  of  one  pea,  into  a  straight  line,  an 
obtuse,  right,  and  acute  angle.  What  has  been 
said  in  regard  to  laying  of  staffs  in  connection 
with  Fig.  I — 23  on  Plate  XXX.  will  ser\'e 
here  also. 

Of  three  wires,  a  longer  line  is  formed ; 
angles,   with  one   long,  and  one  short  side. 


72 


GUIDE  TO  KINDER- GARTNERS. 


The  three  wires  are  introduced  into  one  pea, 
so  that  they  meet  in  one  point ;  two  parallel 
lines  may  be  continued  by  a  third  ;  finally  the 
equilateral  triangle  is  produced. 

Then  follows  the  square,  parallelogram, 
rhomboid ;  diagonals  may  be  drawn  and  the 
forms  shown  on  Plate  LXXII..  figures  i — lo, 
be  produced.  The  possibility  of  representing 
the  most  manifold  forms  of  knowledge,  of  life 
and  of  beauty,  is  reached,  and  the  forms  pro 
duced  may  be  used  for  other  purposes.  The 
;hild  may  produce  six  triangles  of  equal  size, 
and  repeat  with  them  all  the  exercises,  gone 
through  with  the  tablets,  and  may  enlarge 
upon  them. 

Or  the  child  iiiay  prepare  4.  8,  16  right  an- 
gled triangles,  or  obtuse  angled,  or  acute  an- 
gled triangles  and  lay  with  them  the  figures 
given  on  Plate  LXXII.,  etc ,  for  the  course  of 
drawing,  and  carry  them  out  still  further. 

After  these  hints  it  seems  impossible  not 
to  occupy  the  child  in  an  interesting  and  in- 
structive manner. 

But  the  condition  attached  to  each  new  Gift 
of  the  Kinder-Garten  is  some  special  progress 
in  its  course. 

We  produced  outlines  of  many  objects  with 
the  staffs  ;  all  formations,  however,  remained 
planes,  whose  sides  were  represented  by  staffs. 
In  the  working  with  peas,  the  wires  represent 
edges,  the  peas  serve  as  corners,  and  these 
skeleton  bodies  are  so  much  more  instructive 
as  they  allow  the  observation  of  the  outer 
forms  in  their  outlines,  and  the  inner  structure 
and  being  of  the  body  at  the  same  time. 

The  child  unites  two  equilateral  triangles 
by  three  equally  long  wires,  and  forms  thereby 
a  prism,  (Fig.  14;)  four  equilateral  triangles, 
give  the  three-sided  pyramid;  eight  of  them, 
the  octahedron.     (Figs.  15  and  16.) 

From  two  equal  squares,  united  by  four 
wires  of  the  length  of  the  sides,  the  skele- 
ton cube,  Fig.  17,  is  formed;  if  the  uniting 
wires  are  longer  than  the  sides  of  the  square, 
the  four  sided  column  (Fig.  8);  is  one  of  the 
squares  larger  than  the  other,  a  topless  pyra- 
mid will  be  produced,  etc. 


It  is  hardly  possible  that  pupils  of  the 
Kinder  Garten  should  make  any  further  prog- 
ress in  the  formation  of  these  mathematical 
forms  of  crystallization,  as  the  representation 
of  the  many-sided  bodies,  and  especially  the 
development  of  one  from  another,  requires 
greater  care  and  skill  than  should  be  expected 
at  such  an  early  period  of  life.  It  will  be  re 
served  for  the  primary,  and  even  a  higher 
grade  of  school,  to  proceed  farther  on  the 
road  indicated,  and  in  this  manner  prepare 
the  pupil  for  a  clear  understanding  of  regular 
bodies.  (  Fig.  ig  shows  how  the  octahedron 
is  contained  in  the  cube.) 

This,  however,  does  not  exclude  the  con- 
struction by  the  more  advanced  pupils  of  the 
Kinder-Garten,  of  simple  objects,  in  their 
surroundings,  such  as  benches,  (Fig.  21,) 
chairs,  (Fig.  23,)  baskets,  etc  ,  or  to  try  to 
invent  other  objects. 

Whoever  has  himself  tried  peas-work,  will 
be  convinced  of  its  utility.  Great  care,  much 
patience,  are  needed  to  produce  a  somewhat 
complicated  object ;  but  a  successful  structure 
repays  the  child  for  all  painstaking  and  per- 
severance. By  this  exercise,  the  pupils  im- 
prove in  readiness  of  construction,  and  this 
is  an  important  preparation  for  organiza 
tion. 

More  advanced  pupils  try  also,  success- 
fully, to  construct  letters  and  numerals,  with 
the  material  of  this  Gift. 

The  bodies  produced  by  peas  work "  may 
be  used  as  models  in  the  modeling  depart- 
ment. The  one  occupation  is  the  comple- 
ment of  the  other.  The  skeleton  cube  allows 
the  observation  of  the  qualities  of  the  solid 
cube,  in  greater  distinctness.  The  image  of 
the  body  becomes  in  this  manner  more  per- 
fect and  clear,  and  above  all,  the  child  is 
led  upon  the  road,  on  which  alone  it  is 
enabled  to  come  into  possession  of  a  true 
knowledge  and  correct  estimate  of  things ; 
the  road  on  which  it  learns,  not  only  to  ob- 
serve the  external  appearance  of  things,  but 
in  the  meantime,  and  always,  to  look  at  their 
internal  being. 


THE    TWENTIETH    GIFT. 


MATERIAL  FOR  MODELING. 


(plate  lxxiv.) 


Modeling,  or  working  in  clay,  held  in  high 
estimation  by  Froebel,  as  an  essential  part  of 
the  whole  of  his  means  of  education  is,  strange 
to  say,  much  neglected  in  the  Kinder-Garten. 
As  the  main  objection  to  it  named  is  that  the 
children,  even  with  the  greatest  care,  can  not 
prevent  occasionally  soiling  their  hands  and 
their  dothes.  Others,  again,  believe  that  an 
occupation,  directly  preparing  for  art,  very 
rarely  can  be  continued  in  life.  They  call  it, 
therefore,  aimless  pastime  without  favorable 
consequences,  either  for  internal  development 
or  external  happiness. 

If  it  must  be  admitted  that  the  soiling  of 
the  hands  and  clothing  cannot  always  be 
avoided,  we  hold  that  for  this  very  reason, 
this  occupation  is  a  capital  one,  for  it  will 
give  an  opportunity  to  accustom  the  children 
to  care,  order  and  cleanliness,  provided  the 
teacher  herself  takes  care  to  develop  the  sense 
of  the  pupils,  for  these  virtues,  in  connection 
with  this  occupation ;  as  on  all  other  occasions, 
she  should  strive  to  excite  the  sense  of  clean- 
liness as  well  as  purity.  Certainly,  parts  of 
the  adhesive  clay  will  stick  to  the  little  fingers 
and  nails  of  the  children,  and  their  wooden 
knives ;  but,  pray,  what  harm  can  grow  out  of 
this?  The  child  may  learn  even  from  this 
fact.  Tt  may  be  remarked  in  connection  with 
it,  that  the  callous  hand  "of  the  husbandman, 
the  dirty  blouse  of  the  mechanic,  only  show 
the  occupation,  and  cannot  take  aught  from 
the  inner  worth  of  a  man.  As  regards  the  ob- 
jection to  this  occupation  as  aimless  and 
without  result,  it  should  be  considered  that 


occupation  W'ith  the  beautiful,  even  in  its 
crudest  beginnings,  always  bears  good  fruit, 
because  it  prepares  the  individual  for  a  true 
appreciation  and  noble  enjoyment  of  the 
same.  Just  in  this  the  significance  of  Froebel's 
educational  idea  partly  rests,  that  it  strives  to 
open  every  human  heart  for  the  beautiful 
and  good — that  it  particularly  is  intended  to 
elevate  the  social  position  of  the  laboring 
classes,  by  means  of  education,  not  only  in 
regard  to  knowledge  and  skill,  but  also,  in 
regard  to  a  development  of  refinement  and 
feeling. 

Representing,  imitating,  creating,  or  trans- 
forming in  general,  is  the  child's  greatest  en- 
joyment. Bread-crumbs  are  modeled  by  it 
into  balls,  or  objects  of  more  complicated 
form,  and  even  when  biting  bits  from  its 
cooky,  it  is  the  child's  desire  to  produce 
form.  If  a  piece  of  wax,  putty,  or  other  plia- 
ble matter,  falls  into  its  hands,  it  is  kneaded 
until  it  assumes  a  form,  of  which  they  may 
assert  that  it  represents  a  baby, — the  dog 
Roamer.  or  what  not !  Wet  sand,  they  press 
into  their  little  cooking  utensils,  when  playing 
"house-keeping,"  and  pass  off  the  forms  as 
puddings,  tarts,  etc. ;  in  one  word,  most  chil- 
dren are  born  sculptors.  Could  this  fact  have 
escaped  Froebel's  keen  observation.-'  He 
has  here  provided  the  means  to  satisfy  this 
desire  of  the  child,  to  develop  also  this  talent, 
in  its  very  awakening. 

According  to  Froebel's  principle,  the  first 
exercises  in  modeling  are  the  representation 
of  the  fourteen  stereometric  fundamental  forms 


74 


GUIDE  TO   KINDER  GARTNERS. 


of  crj'stallization,  which  he  presents  in  a  box, 
by  themselves  as  models.  Starting  from  the 
cube  the  cylinder  follows — then  the  sphere 
Pyramiii  \\\\\\  3.  4  and  6  sides,  ihe  prism  in  its 
various  formations  of  planes,  the  octahedron 
or  decahedron  and  cosahedron,  or  bodies  with 
8,  12  and  20  equal  sides  or  faces,  etc.,  etc. 
However  interesting  and  instructive  this  course 
may  be.  we  prefer  to  begin  with  somewhat 
simpler  performances,  leaving  this  branch  of 
this  department  for  future  time. 

The  child  receives  a  small  quantity  of  clay, 
(wax  may  also  be  used,)  a  wooden  knife,  a 
small  board,  and  a  piece  of  oiled  paper,  on 
which  it  performs  the  work.  If  clay  is  used, 
this  material  should  be  kept  in  wet  rags,  in 
a  cool  place,  and  the  object  formed  of  it, 
dried  in  the  sun,  or  in  a  mildly-heated  stove, 
and  then  coated  with  gum  arable,  or  var- 
nish, which  gives  them  the  appearance  of 
crockery. 

First,  the  child  forms  a  sphere,  from  which  it 
may  produce  many  objects.  If  it  attaches  a 
stem  to  it,  it  is  a  cherry;  if  it  adds  depressions 
and  elevations*  which  represent  tiie  dried  calyx^ 
it  will  look  like  an  apple  ;  from  it  the  pear,  nut, 
potato,  a  head,  may  be  molded,  etc.  Many 
small  balls  made  to  adhere  to  one  another 
may    produce    a    bunch    of    grapes,    (Figs. 

From  the  ball  or  sphere,  a  cylindrical  body 
may  be  formed,  by  rolling  on  the  board,  usu- 
ally called  by  the  children  a  loaf  of  bread, 
cigar,  a  candle,  loaf  of  sugar,  etc. 

A  bottle,  a  bag  filled  with  flour  or  some- 
thing else,  can  also  easily  be  produced. 

Very  soon  the  child  will  present  the  cube, 
an  old  acquaintance  and  playmate.  From  it, 
it  produces  a  house,  a  box.  a  coffee  mill  and 
similar  things.  Soon  other  forms  of  life  will 
grow  into  existence,  as  plates,  dishes,  animals 
and  human  beings,  houses,  churches,  birds' 
nests,  etc..  etc.  If  this  occupation  is  intended 
to  be  more  than  mere  entertainment,  it  is 
necessary  to  guide  the  activity  of  the  child  in 
a  definite  direction 

The  best  direction  to  be  followed  in  Froe- 


bel's  occupations  is  that  for  the  development 
of  regular  forms  of  bodies  Fundamental 
form,  of  course,  is  the  sphere.  The  child 
represents  it  easily,  if  perhaps  not  exactly 
true. 

By  pressing  and  assisted  by  his  knife,  the 
one  plane  of  the  sphere  is  changed  to  several 
planes,  corners,  edges,  which  produces  the 
cube'.  If  the  child  changes  its  corners  to 
planes  (indicated  in  Fig.  12,)  a  form  of  four^ 
teen  sides  is  produced.  If  this  process  is 
continued  so  that  the  planes  of  the  cube  are 
changed  to  corners,  the  octahedron  is  the  re- 
sult, (Fig.  13.)  By  continued  change  of  edges 
to  planes  and  of  planes  to  corners,  the  most 
important  regular  forms  of  crystallization  will 
be  produced,  which  occupation,  however,  as 
mentioned  before,  belongs  rather  to  a  higher 
grade  of  school,  and  is  therefore  better 
postponed  until  after  the  Kinder-Garten 
training. 

Some  regular  bodies  are  more  easily 
formed  from  the  cylinder,  the  mediation  be- 
tween the  sphere  and  cube.  By  a  pressure  of 
the  hand,  or  by  means  of  his  knife,  the  child 
changes  the  one  round  plane  to  three  or  four 
planes,  and  as  many  edges,  producing  thereby 
the  prism  and  the  four-sided  column. 

If  we  change  one  of  the  planes  of  the  cyl- 
inder to  a  corner,  by  forming  a  round  plane 
from  its  center  to  the  periphery  of  the  plane, 
we  produce  a  cone.  If  we  change  the  sur- 
face of  the  cone  to  three  or  four  planes,  we 
shall  have  a  three  or  four  sided  pyramid.  If 
we  act  in  the  same  manner  with  the  other  end 
of  the  cylinder,  we  shall  form  a  double  cone, 
and  from  it  we  may  produce  a  three  or  four- 
sided  double  pyramid,  etc.  If  we  act  in  an 
opposite  manner,  destroy  the  edges  of  the 
cylinder,  we  shall  again  have  the  sphere. 

Well  formed  specimens  may,  to  acquire 
greater  durability,  be  treated  as  indicated 
previously.  The  production  of  forms  and  fig- 
ures from  soft  and  pliable  material  belongs, 
undoubtedly,  to  the  earliest  and  most  natural 
occupations  of  the  human  race,  and  has  served 
all  plastic  arts  as  a  starting-point.     The  occu 


GUIDE  TO   KINDER-GARTNERS. 


75 


pation  of  modeling,  then,  is  eminently  fit  to 
carry  into  practice  Froebel's  idea  that  chil- 
dren, in  their  occupations,  have  to  pass  through 
all  the  general  grades  of  development  of  hu- 
man culture  in  a  diminished  scale.  The 
natural  talent  of  the  future  architect  or  sculp 
tor,  lying  dormant  in  the  child,  must  needs  be 
called  forth  and  developed  by  this  occupation, 
as  by  a  self-acting  and  inventing  construction 
and  formation,  all  innate  talents  of  the  child 
are  made  to  grow  into  visible  reality. 


If  we  now  cast  a  retrospective  look  upon 
the  means  of  occupation  in  the  Kinder- 
Garten,  we  find  that  the  material  progresses 
form  the  solid  and  whole,  in  gradual  steps  to 
its  parts,  until  it  arrives  at  the  ifnage  upon 
the  plane,  and  its  conditions  as  to  line  and 
point.  For  the  heavy  material,  fit  only  to  be 
placed  upon  the  table  in  unchanged  form, 
(the  building  blocks.)  a  more  flexible  one 
is  substituted  in  the  following  occupations: 
wood  is  replaced  by /<z/<?/'.  The  paper  plane 
of  the  folding  occupation,  is  replaced  by  the 
paper  strip  of  the  weaving  occupation,  as  line. 
The  wooden  staff,  or  very  thin  wire,  is  then 
introduced  for  the  purpose  of  executing  per- 
manent figures  in  connection  with  peas,  repre- 
senting the  point.  In  place  of  this  material 
the  draivn  line  then  appears,  to  which  colors 
are  added.  Perforating  and  embroidering 
introduces  another  addition  to  the  material 
to  create  the  images  of  fantasy,  which,  in  the 
paper  cutting  and  mounting,  again  receive 
new  elements. 

The  tnodeling  in  clay,  or  wax,  affords  the  im- 
mediate plastic  artistic  occupation,  with  the 
most  pliable  material  for  the  hand  of  the 
child.  Song  introduces  into  the  realm  of 
sound,  when  movement  plays,  gymnastics,  and 
dancing,  help  to  educate  the  body,  and  insure 
a  harmonious  development  of  all  its  parts. 
In  practicing  the  technical  manual  perform- 
ances of  the  mechanic,  such  as  boring, 
piercing,  cutting,  measuring,  uniting,  forming, 
drawing,  painting,  and  modeling,  a  foundation 
of  all  future  occupation  of  artisan  and  artist 


— synonymous  in  past  centuries — is  laid.  For 
ornamentation  especially,  all  elements  are 
found  in  the  occupations  of  the  Kinder  Gar- 
ten, The  forms  of  beauty  in  the  paper-fold- 
ing./ i ,  serve  as  series  of  rosettes  and  or- 
naments in  relief,  as  architecture  might  em- 
ploy them,  without  change.  The  productions 
in  the  braiding  department  contain  all  con- 
ditions of  artistic  weaving,  nor  does  the  cut- 
.ting  of  figures  fail  to  afford  richest  material 
for  ornamentation  of  various  kinds. 

For  every  talent  in  man.  means  of  develop- 
ment are  provided  in  the  Kinder-Garten  ma- 
terial, opportunity  for  practice  is  constantly 
given,  and  each  direction  of  the  mind  finds 
its  starting-point  in  concrete  things.  No  more 
complete  satisfaction,  therefore,  can  be  given 
to  the  claim  of  modern  pedagogism,  that  all 
ideas  should  be  founded  on  previous  percep- 
tion, derived  from  real  objects,  than  is  done  in 
the  genuine  Kinder  Garten. 

Whosoever  has  acquired  even  a  superfi- 
cial idea  only  of  the  significance  of  P'roebel's 
means  of  occupation  in  the  Kinder-Garten, 
will  be  ready  to  admit  that  the  ordinary  play- 
things of  children  can  not,  by  any  means,  as 
regards  their  usefulness,  be  compared  with 
the  occupation  material  in  the  Kinder-Gar- 
ten. That  the  former  may,  in  a  certain  de- 
gree, be  made  helpful  in  the  development  of 
children,  is  not  denied  ;  occasional  good  re- 
I  suits  with  them,  however,  mostly  always  will 
be  found  to  be  owing  to  the  child's  own  in 
stinct  rather  than  to  the  nature  of  the  toy. 
Planless  playing,  without  guidance  and  super- 
vision cannot  prepare^a  child  for  the  earnest 
sides  of  life  as  well  as  for  the  enjoyment  of 
its  harmless  amusements  and  pleasures. 
Like  the  plant,  which,  in  the  wilderness  even, 
draws  from  the  soil  its  nutrition,  so  the  child's 
mind  draws  from  its  surroundings  and  the 
means,  placed  at  its  command,  its  educational 
food.  But  the  rose-bush,  nursed  and  cared 
for  in  the  garden  by  the  skillful  horticulturist 
produces  flowers,  far  more  perfect  and  beau- 
tiful than  the  wild  growing  sweet  briar.  With- 
out care  neither  mind  nor  body  of  the  child 


76 


GUIDE  TO   KINDER-GARTNERS. 


can  be  expected  to  prosper.  As  the  latter 
can  not,  for  a  healthful  development,  use  all 
kinds  of  food  without  careful  selection,  so 
the  mind  for  its  higher  cultivation  requires  a 
still  more  careful  choice  of  the  means  for  its 
development.  The  child's  free  choice  is  lim- 
ited only  in  so  far  as  it  is  necessary  to  limit 
the  amount  of  occupation  material  in  order 
to  fit  it  for  systematic  application.  The  child 
will  find  instinctively  all  that  is  requisite  for 
its  mental  growth,  if  the  proper  material  only 
be  presented,  and  a  guiding  mind  indicate  its 
most  appropriate  use  in  accordance  with  a 
certain  law. 

Froebel's  genius  has  admirably  succeeded 
in  inventing  the  proper  material  as  well  as  in 
pointing  out  its  most  successful  application  to 
prepare  the  child  for  all  situations  in  future 
life,  for  all  branches  of  occupation  in  the 
useful  pursuits  of  mankind. 


When  the  Kinder-Garten  was  first  estab- 
lished by  him,  it  was  prohibited  in  its  original 
form  and  its  inventor  driven  from  place  to 
place  in  his  fatherland  on  account  of  his  lib- 
eral educational  principles,  to  be  carried  out 
in  the  Kinder  Garten.  The  keen  eye  of  mo- 
narchial  government  ofiicials  quickly  saw  that 
such  institution  could  not  turn  out  willing 
subjects  to  tyrannical  oppression,  and  the  ru- 
lers '■'■by  the  grace  of  God,'''  tolerated  the 
Kinder-Garten,  only  when  public  opinion  de- 
clared too  strongly  in  its  favor. 

In  pleading  the  cause  of  the  Kinder-Gar- 
ten on  the  soil  of  republican  America,  is  it 
asking  too  much  that  all  may  help  in  extend- 
ing to  the  future  generation  the  benefits  which 
may  be  derived  from  an  institution  so  emi- 
nently fit  to  educate  free  citizens  of  a  free 
country  ? 


KINDER-GARTEN  CULTURE. 


The  fundamental  principle  of  the  Kinder-Garten 
system  of  education,  so  clearly  laid  down  in  his  writ- 
ings, and  so  successfully  carried  out  in  practice  by 
Friedrich  Froebel,  is  expressed  in  the  axiom,  that,  be- 
fore ideas  can  be  defined,  perceptions  must  have  pre- 
ceded ;  objects  must  have  been  presented  to  the  sen- 
ses, and  by  their  examination  experiences  acquired 
of  their  being,  quality  and  action,  of  which  definite 
ideas  are  the  logical  results,  with  which  they  are  there- 
fore inseparably  connected.  It  is  not  claimed  that 
this  principle  origiixated  with  the  inventor  of  the  Kin- 
der Garten  ;  for  long  before  him  it  was  said  that: 
"  Nihil  esi  in  intellectu,  quod  antea  non  fuerit  in  sensu," 
but,  in  the  Kinder-Garten  system,  he  has  furnished  all 
material  to  begin  the  education  of  mankind  on  this 
logical  basis. 

L'efinite  ideas  are  to  originate  as  abstractions  from 
perceptions.  (Aiischauungen,  as  the  Germans  say, 
meaning  literally  the  looking  at,  or  into  things.)  If  they 
do  not  originate  in  such  manner  they  are  not  the  prod- 
uct of  one's  own  mental  activity,  but  simply  the  consent 
of  the  understanding  to  the  ideas  of  others.  By  far 
the  greatest  part  of  all  acquired  knowledge  with  the 
mass  of  the  people,  is  of  this  kind.  Every  one,  how- 
ever, even  the  least  gifted,  may  acquire  a  stock  of 
fundamental  perceptions,  which  shall  serve  as  points 
of  relation  in  the  process  of  thinking.  Indefinite  or 
confused  fundamental  or  elementary  perceptions  pre- 
vent understaTiding  words  with  precision,  which  is  nec- 
essary to  reflecting  on  the  ideas  and  thoughts  of  others 
with  clearness,  and  appropriating  them  to  one's  self. 
In  the  fact  that  a  large  majority  of  persons  are  lacking 
in  clear  and  distinct  fundamental  perceptions,  we  find 
cause  for  the  existence  of  so  many  confused  heads, 
full  of  the  most  absurd  notions.  The  period  of  life 
in  which  the  first  fundamental  perceptions  are  formed 
must  necessarily  be  our  earliest  childhood.  They  can 
form  only  during  this  state  of,  as  it  were,  mental  un- 
consciousness, because  the  impressions  on  the  senses 
can  best  be  fixed  lastingly  upon  the  soul,  when  this 
process  is  least  disturbed  by  reflection  ;  and  impres- 
sions of  objects  of  the  world  without  upon  our  senses, 
are  made  more  or  less  clearly  and  distinctly,  accord- 
ing to  the  nature  of  these  objects  themselves.  A  mere 
acquisition  of  perceptions,  however,  is  not  sufficient. 


As  in  the  development  of  all  organism  in  nature,  a 
certain,  peculiar  series  of  events  takes  place,  which 
always  must  be  the  same,  or  at  least  take  place  in  ac- 
cordance with  the  same  law,  to  reach  the  same  aim, 
or  produce  the  same  form ;  so,  also,  in  mental  devel- 
opment, a  peculiar  process,  a  natural  series  of  events 
must  take  place  without  disturbing  occurrences,  to 
successfully  reach  the  corresponding  idea  in  the  mind. 
This  series  of  events  in  the  mind  and  heart,  connected 
with  the  process  of  thinking,  is  in  philosophy  ex- 
plained to  consist  of:  ist.  A  general  or  total  impres- 
sion. 2d  A  perception  or  looking  on  a  singjjc  thing. 
3d.  Observation  of  qualities  and  relations.  4th.  Com- 
parison. 5th.  Judging.  6th.  Conclusion.  Although 
a  right  selection  of  objects,  and  their  proper  succes- 
sion, are  of  the  first  importance,  adherence  to  these 
two  conditions  is  not  yet  sufficient  to  prepare  and  ac- 
custom the  mind  to  logical  thinking ;  these  means 
should  be  applied  or  presented  in  a  systematic,  me- 
thodical way,  also.  A  system  of  education  in  perfect 
accordance  with  the  laws  of  nature  is  only  possible, 
therefore,  when  the  modus  operandi  of  the  natural 
functions  of  the  soul,  during  their  development,  is  fully 
understood,  and  the  exact  means  are  discovered  to 
assist  these  functions  in  a  corresponding  manner  from 
without.  As  long  as  this  is  not  done,  the  education 
of  the  human  race  is  left  to  be  the  result  of  chance, 
and  at  the  mercy  of  mere  educational  instinct.  We 
claim  that  the  significance  of  Froebel's  educational  sys- 
tem consists  mainly  in  a  perfect  understanding  of  the 
natural  process  of  mental  development.  This  under- 
standing guided  him  in  preparing  certain  means  of 
education,  or  play,  all  following  the  same  course  as 
the  mental  development  which  they  are  intended  to 
promote.  No  man  has  ever  looked  so  deeply  as 
Friedrich  Froebel  into  the  secret  workshop  of  a  child's 
soul,  and  so  successfully  discovered  the  means  and 
their  methodical  application  for  a  development  of  the 
young  mind  in  accordance  with  nature's  own  laws. 
To  be  certain  that  the  natural  course  of  development 
be  not  interrupted  but  logically  assisted,  the  child's 
instinct  should  have  free  choice  within  appointed 
limits,  and  still  be  obliged  to  receive  the  objects  as 
they  are  presented  to  it  for  the  first  perceptions.  The 
means  to  obtain  this,  Froebel  has  found  in  allowing 


78 


KINDER-GARTEN   CULTURE. 


the  child  to  manipulate  the  things  destined  for  the 
production  of  changes  according  to  his  own  choice. 
Thereby  the  child  will  be  led  to  devote  attention  to 
the  objects  formed,  because  he  looks  upon  them  as  his 
own  work,  and  rejoices  in  what  he  is  able  to  do.  That 
free  unrestricted  activity  of  the  child,  which  we  call 
play,  alone  can  comply  with  these  conditions;  any 
thing  e.\se  forced  upon  the  child,  can  never  be  success- 
fully employed  for  this  purpose.  A  desire  of  acquir- 
ing knowledge  of  things,  is  an  innate  faculty  of  the 
soul,  hence  there  is  no  need  oi  forchtg  ihe  child  into 
making  acquaintance  with  the  things  given  him  to 
play  with.  We  have  only  to  select  for  his  playthings 
the  fundamental  forms,  which,  like  the  typical  forma- 
tions in  nature,  offer,  as  it  were,  a  fundamental  scheme 
for  an  acquaintance  with  the  large  multitude  of  things 
Knowledge  of  things  can  be  acquired  only  by  acqui- 
sition of  a  knowledge  of  their  qualities.  We  then 
have  to  provide  ojects  in  which  the  general  qualities 
of  things  are  shown  in  perfect  distinctness,  in  order 
to  produce  thereby  clear  and  lasting  perceptions  in 
the  mind  of  the  child.  These  objects  should  be  such 
that  they  may  be  easily  manipulated  by  the  limited 
strength  of  the  child,  that  he  may  become  acquainted 
with  them  by  their  use,  and  become  enabled  thereby 
to  gather  experiences  in  regard  to  events  and  facts  in 
the  physical  world,  and  may,  so  to  say,  serve  him  for 
the  first  physical  experiments.  Examining  the  list  of 
Froebel's  Kinder-Garten  occupation  material,  we  find 
it  to  consist  of  the  following : 

1.  Six  soft  balls  of  various  colors. 

2.  Sphere,  cube,  and  cylinder,  made  of  wood. 

3.  Large  cube,  divided  into  eight  small  cubes. 

4.  Large  cube,  divided  into  eight  oblong  blocks. 

5.  Large  cube,  consistjng  of  21  whole,  6  half  and 
12  quarter  cubes. 

6.  Large  cube,  consisting    of   18  whole  oblongs 
with  3  divided  lengthwise  and  6  divided  breadthwise. 

7.  Quadrangular,  and  various  triangular  tablets 
for  laying  figures. 

8.  Staffs  or  wands  for  laying  figures. 

9.  Whole  and  half  wire  rings  ior  laying  figures. 

10.  Material  for  drawing. 

11.  Material  for  perforating. 

12.  Material  for  embroidering. 

13.  Material  for  paper  cutting  and  combining  the 
parts  into  symmetrical  figures. 

14.  Material  for  weaving  or  braiding. 

15.  Slats  for  interlacmg. 


16.  Slats  with  4,  6,  8,  and  16  links. 

17.  Paper  strips  for  lacing. 

18.  ilaterial  for  paper  folding. 

19.  Material  for  peas  work. 

20.  Material  for  modeling.* 

The  list  begins  with  the  ball,  an  object,  comprising 
in  itself,  in  the  simplest  manner,  the  general  qualities 
of  all  things.  As  the  starting  point  of  form — the 
spherical — it  gives  the  first  impression  of  form,  and 
being  the  most  easily  moved  of  all  forms,  is  symboli- 
cal of  life.  It  becomes  the  first  known  object,  with 
which  all  other  objects  for  the  child's  play  are  brought 
into  relation.  Beside  teaching  form,  the  balls  are 
also  intended  to  teach  color,  hence  their  number  of 
six,  representing  three  primary  and  three  secondary 
colors.  The  principle  of  combining,  uniting,  or  bring- 
ing into  relation  of  opposites,  which  is  a  governing  law 
throughout  all  occupations  in  the  Kinder-Garten,  is 
applied  here  to  discriminating  primary  and  secondary 
colors,  the  latter  being  produced  by  a  coQibination  of 
two  of  the  former.! 

For  the  purpose  of  acquiring  clear  and  distinct, 
correct  ideas  of  things  around  us,  it  is  indispensably 
necessary  to  become  acquainted  with  them  in  all  res- 
pects and  relations.  The  balls  are  made  the  object 
of  a  great  variety  of  plays  or  occupations,  to  make 
the  child  become  well  acquainted  with  its  uses,  and 
to  enable  him  to  handle  it  gracefully.  Then,  for  the 
purpose  of  comparison,  the  second  Gift  is  introduced, 
consisting  of  sphere,  cu^e,  and  cylinder.  We  can  here, 
certainly  not  yet  speak  of  a  rational  comparison  on 
the  part  of  the  young  child,  but  simply  of  an  imme- 
diate, sensual  perception  or  observation  of  the  simi- 
larities and  differences  existing  in  the  things  pre- 
sented. The  child  will  find  by  looking  at  the  three 
new  objects  exhibited  to  him  that  the  sphere  is  just 
like  the  ball,  except  in  its  material.  The  first  impres- 
sion, that  of  roundness,  made  upon  the  child  by  the 
many  colored,  soft  balls,  finds  here  its  further  devel- 
opment by  the  fact  that  this  quality  is  found  in  this 
wooden  ball,  or  the  sphere,  as  he  may  be  led  to  name 
it,  learning  a  new  word.  To  facilitate  the  process  of 
comparison,  the  objects  to  be  compared  should  first 
be  as  different  as  possible,  opposites  in  a  certain  sense. 
The  opposition  between  sphere  and  cube  relates  to 
their  form.  Together  with  the  oppositional,  or  dif- 
ference in  objects,  their  similarity  should  in  the  mean- 
time be  made  prominent,  for  comparison  demands  to 
detect  equality  and  similarity  of  things  as  well  as  their 


♦The  above  arrangement  and  numbering  of  the  Gifts,  adopted  by  writers  on  the  Kinder-Garten,  and  manufacturers  of  its  occupation 
material,  has  been  retained  here,  as  a  change  could  not  well  be  made  without  producing  much  confusion.  The  logical  connection  of  the 
Gifts,  as  described  in  this  paper,  can  not  be  affected  in  the  least  by  the  numbers  attached  to  them  for  the  purpose  of  designating  them  as 
articles  of  manufacture. 

t  When  the  secondary  colors  are  presented,  it  would  be  well  to  have  three  pieces  of  glass  of  the  three  primary  colors,  and  let  the  chil- 
dren take  two  and  look  through  them  toward  the  light,  which  would  teach  them  sensuously  the  combinations. 


KINDER-GARTEN   CULTURE. 


79 


distinction  by  inequality  and  dissimilarity.  The  cyl- 
inder introduced  as  the  mediatory  between  the  oppo- 
sites  in  form,  given  here,  is  the  simplest  and  imme- 
diately suggested  mediative  form,  because  it  com- 
bines the  qualities  of  both  cube  and  sphere  in  itself. 

These  three  'u>hole  bodies,  introduced  as  fundamen- 
tal or  normal  forms  or  shapes,  in  which  all  quali- 
ties of  whole  bodies  in  general  are  demonstrated,  and 
which  serve  to  convey  the  idea  of  an  impression  of 
the  whole,  are  followed  by  the  introduction  oi  variously 
divided  solid  bodies.  Without  a  division  of  the  whole, 
observation  and  recognition,  i.  e.,  knowledge  of  it,  is 
next  to  impossible.  The  rational  investigation,  the 
dissecting  and  dividing  by  the  mind,  in  short,  the 
analysis  should  be  preceded  by  a  like  process  in  real 
objects,  if  the  mind  is  calculated  to  reflect  upon 
nature.  Division  performed  at  random,  however,  can 
never  give  clear  ideas  of  the  whole  or  its  parts,  but  a 
regular  division,  in  accordance  with  certain  laws,  is 
always  needed.  Nature  gives  us  also  here  the  best 
instruction.  She  performs  all  her  divisions  according 
to  mathematical  laws. 

Tiie  orders  in  the  vegetable  kingdom  are  distin- 
guished according  to  form  and  number  of  parts. 
Froebel  here,  also,  borrowed  from  nature  a  guide 
which  led  him  in  systematizing  the  means  of  devel- 
opment of  the  yourg  mind  in  the  Kinder-Garten. 

As  the  first  divided  body,  a  large  cube  is  intro- 
duced, consisting  of  eight  small  cubes  of  the  same 
size  each,  as  its  parts.  The  large  cube  is  divided 
once  in  each  direction  of  space,  lengthwise,  breadth- 
wise and  hightwise.  The  form  of  the  parts  is  here 
like  the  form  of  the  whole,  and  only  their  relation  as 
to  volume  is  different.  In  shape,  alike,  they  differ  in 
size,  which  fact  becomes  more  apparent  by  a  variety 
of  combinations  of  a  different  number  of  the  parts. 
Thus  the  relation  of  number  is  here  introduced  to 
the  observation  of  the  child,  together  with  that  of 
form  and  magnitude.  A  clear  and  distinct  idea  of 
these  relations  could  hardly  be  attained  unless  pre- 
sented in  this  manner.  In  the  following  Gift,  diver- 
sity of  form'  in  the  whole  and  its  jjarts,  is  made  ap- 
parent, preceding  the  introduction  of  the  relations  of 
the  plane.  The  logical  connection  with  the  preced- 
ing Gifts  consists  in  the  same  form  of  the  whole,  the 
cube,  and  the  same  manner  of  division  ;  the  5th  and 
6th  being  divided  twice,  whereas  the  3d  and  4th  were 
divided  only  once  in  all  directions  of  space.  The* 
variety  of  forms  gained,  by  this  division  of  the  cube, 
give  the  widest  scope  to  the  invention  and  production 
of  combined  forms,  without  ever  leading  to  an  indefi- 
nite, unlimited,  unrestrained  activity.  The  logical 
combination  of  parts  to  a  whole,  which  is  required  in 
using  these  blocks,  renders  it  a  preparatory  occupation 
for  succeeding  combinations  of  thought,  for,  also  the 


construction  of  parts  into  a  whole  follows  certain  laws, 
thereby  forming  a  serial  connection,  which,  in  nature, 
is  represented  by  the  membering  or  linking  of  all  or- 
ganisms. As  nature,  in  the  organic  world,  begins  to 
form  by  agglomeration,  so  the  child  in  its  first  occu- 
pations commences  with  mere  accumulation  of  parts. 
Order,  however,  is  requisite  to  lead  to  the  beautiful 
in  the  visible  world,  as  logic  is  indispensable  in  the 
world  of  thought  for  the  formation  of  clear  ideas ; 
and  Froebel's  law  to  link  opposites,  affords  the  simplest 
and  most  reliable  guide  to  this  end. 

In  the  building  occupation  this  law,  f  i.,  is  applied 
in  relation  to  the  joining  of  blocks  according  to  their 
form,  or  the  different  position  of  the  parts  in  relation 
to  a  commoiv  center.  If  I  join  sides  and  sides,  or 
edges  and  edges  of  the  blocks,  I  have  formed  oppo- 
sites;  side  and  edge  or  edge  and  side  joined,  are  con- 
sidered as  links  or  mediation.  Thus  below  and  above 
are  opposites  in  relation  to  which  the  right  and  left  side 
of  form  or  figure  built,  serve  as  mediative  parts.  Car- 
rying out  this  principle,  we  have  established  a  most 
admirable  order,  by  which  even  the  youngest  pupil, 
frequently  unknowingly,  produces  the  most  charming 
regular  forms  and  figures.  This  regular  and  serial 
constructing  of  the  parts  to  a  whole,  according  to  a 
determinate  law,  is  followed  by  connecting  various 
wholes  with  one  another,  to  produce  orders  and  series 
as  we  find  them  in  all  the  natural  kingdoms,  just  as  we 
are  in  need  of  categories  in  the  process  of  thinking 
Therefore  we  produce  in  the  Kinder-Garten,  by  means 
of  our  occupation  material,  different  series  of  forms 
and  figures  from  common  elementary  forms,  which  we 
call  either  forms  of  life,  forms  of  knowledge,  or  forms 
of  beauty.  The  first  are  representations  of  objects  act- 
ually existing  and  coming  under  our  common  obser- 
vation, as  the  works  of  human  skill  and  art. 

The  second  are  such  as  afford  instruction  relative  to 
number,  order,  proportion,  etc.  The  third  are  figures 
representing  only  ideal  forms,  yet  so  regularly  con- 
structed as  to  present  perfect  models  of  symmetry 
and  order  in  arrangement  of  parts.  By  occupation 
with  these  differently,  yet  always  regularly  constructed 
bodies,  the  child  will  make  observations  of  the  great- 
est variety,  which,  by  immediate  use  of  the  objects 
by  manipulation  and  experiment,  make  a  real  expe- 
rience. The  observations  f  i.  of  the  vertical  and  hor- 
izontal, of  the  right  angled,  of  the  directions  of  up  and 
d  iwiiward,  of  under,  above  and  next  one  another  ;  of 
regularity,  of  equipoise,  the  relation  of  circumference 
and  center,  of  multiplication  and  division,  of  all  that 
produces  harmony  in  construction,  etc.,  impress  them- 
selves, as  it  were,  indelibly  upon  the  child's  mind  almost 
at  every  step.  The  first  knowledge,  or  rather  idea  of 
the  qualities  of  matter,  and  the  first  experiences  of  its 
use,  are  obtained  thus  in  the  simplest  manner  and  de- 


So 


KINDER-GARTEN   CULTURE. 


lightfully.  Thus  the  lawful  shaping,  logical  develop- 
ment and  methodical  application  of  the  material,  is, 
as  it  were,  the  logic  of  nature  imitated,  whose  repre- 
sentation is  found  in  the  forms  of  crystallization.  It 
is  natural  that  the  works  of  God  should  reflect  the 
logic  of  the  great  Creator's  mind,  and  thereby  be  made 
the  teachers  of  mankii;d.  What  can  man  do  better  in 
educating  the  human  mind,  than  imitate  these  means, 
for  the  purpose  'of  unfolding  and  strengthening  the 
germ  of  logic,  implanted  in  the  mind  of  every  human 
being,  created  in  the  image  of  his  God. 

A  condition  of  indisputable  importance  for  the  ac- 
quisition of  knowledge  of  things,  is  the  knowledge  of 
the  material  of  which  they  consist,  and  their  qualities, 
and  this  should  be  introduced  in  right  succession. 
From  the  2d  to  the  6th  Gifts,  the  objects  consist  of 
wood,  and  they  are  in  the  meantime  solid  bodies. 

The  next  step  in  the  use  of  matter  as  the  represen- 
tation of  mind,  is  the  transition  to  the  plane,  Froebel's 
Tablets  for  laying  figures.  In  them,  the  simple  mathe- 
matic  fundamental  forms  are  given  as  embodied 
planes,  beginning  with  the  square,  which  is  followed 
successively  by  the  right-angled  triangle  with  two 
equal  sides,  (1-2  square;)  the  right-angled  triangle 
with  unequal  sides ;  the  obtuse-angled  triangle,  and 
the  equilateral  triangle. 

The  dati  given  for  the  play  of  interlacing  form  the 
transition  from  the  plane  to  the  lint,  resembling  the 
latter,  although,  owing  to  their  width,  still  occupying 
space  as  a  plane.  They  represent  in  one  respect  a 
progress  beyond  the  staffs,  because  they  may  be 
joined  for  the  purpose  of  representing  lastii  g  forms. 

The  staffs,  representing  the  embodied  Inie,  facili- 
tate the  elements  of  drawing,  serving  as  movable  out- 
lines of  planes.  They  are  to  be  looked  upon  as  the 
divided  plane  in  order  to  adhere  to  their  connections 
and  relation  with  the  form  from  which  we  started. 
By  means  of  the  staffs,  numerical  relation  first  is 
made  more  prominent  and  evident  by  the  introduction 
of  figures.  The  application  of  the  law  of  opposiies 
relates  in  all  previous  occupations  to  the  forvi  and 
direction  of  parts. 

In  the  so-called  peas  work  the  staffs  (eventually 
wire)  are  united  by  points,  represented  by  peas,  de- 
monstrating that  it  is  union  which  produces  lasting 
formation  of  matter. 

Here  closes  the  first  section  of  Froebel's  embodied 
alphabet,  intended  to  give  the  elemental  images  for 
the  succeeding  recognition  of  complex  form,  magni- 
tude and  numerical  relations.  Thus  the  child  has 
been  guided  in  a  logical  manner  from  the  solid  body 
through  its  divisions  and  through  the  embodied  plane, 
line  and  point,  in  matter  and  by  matter,  to  the  bor- 
ders of  the  abstract,  without  going  over  into  abstrac- 
tion, which  is  a  later  |)rocess,  to  be  postponed  to  the 


school  that  succeeds  to  the  Kinder-Garten.  To  re- 
duce or  "lead  back"  mathematical  perception  (ab- 
stract thinking;  to  appearances  in  the  material  world, 
no  more  appropriate  means  and  method  could  have 
been  devised.  All  abstractions  are  drawn — abstracted 
according  to  the  original  meaning  of  the  word — from 
manifestations  of  the  visible  world.  Although  further 
final  conclusions  (which  may  be  continued  ad  infini- 
tum) shall  remove  them  from  their  origin,  elevate 
them  to  the  loftiest  hights  of  thought,  their  roots  are 
ever  to  be  looked  for  in  the  material  world.  The 
assertion  that  ideas  are  founded  and  defined  by  per- 
ceptions only,  is  either  entirely  erroneous  and  not  to 
be  proved,  or  there  must  exist  such  a  connection,  such 
an  analogy,  between  the  things  of  the  material  world 
and  the  objects  of  thought,  as  has  been  indicated  here. 
And  if  it  can  be  proved  that  such  a  course  of  devel- 
opment of  the  human  mind  necessarily  takes  place 
in  some  degree  without  our  assistance,  as  a  natural 
process,  then  education  should  not  dare  to  prescribe 
any  other  one  ;  then  this  is  the  only  true  method  of 
developing  the  mind,  because  it  operates  with  nature's 
laws,  although  it  does  not  exclude  all  assistance  on 
our  part,  but  invokes  it.  We  have  often  opportunity 
to  notice  how  easily  the  mind,  without  human  assist- 
ance, grows  in  wrong  directions,  like  the  young  tree 
that  never  felt  the  effect  of  the  pruning-knife. 

In  the  following  occupations  of  the  Kinder-Garten 
we  shall  notice  the  progress  from  the  solid  body  or 
object  itself  io  the  representation  of  its  image  by  draw- 
ing. Planes  and  lines,  the  various  forms  of  the  tri- 
angle and  other  geometric  figures,  occur  also  here, 
but  they  are  produced  by  different  material.  The 
touching  or  handling  of  the  solid  body,  the  most  im- 
portant means  of  acquiring  knowledge  during  the 
first  years  of  a  child's  life,  during  the  state  of  its 
rational  unconsciousness,  is  now  entirely  changed  to 
a  looking  at  objects  presented  to  its  observation ;  and 
the  image  of  the  body,  so  to  say,  takes  the  place  of 
the  body  itself.  Drawing  with  pencil  is  of  such  para- 
mount importance  because  the  child  is  enabled  by  it 
to  reproduce  quickly  and  easily  the  images  imparted 
to  its  mind  by  their  own  visible  representation,  where- 
by they  become  truly  objective  and  are  only  then 
fully  understood.  Instruction  in  writing  should  never 
precede  instruction  in  drawing. 

In  the  development  of  the  human  race,  the  body 
unmistakably  precedes  its  image  or  representation,  as 
the  drawn  image  preceded  the  written  sign  or  letter. 
In  the  incipient  stages  of  civilization,  these  signs  for 
things  were  images,  as  we  see  in  all  hieroglyphic  in- 
criptions.  Our  modern  letters  occupy  the  highest 
step  in  the  scale  of  the  language  of  signs  (which  we 
should  not  forget). 

Froebel's  method  of  instruction  in  drawing  is  as 


KINDER-GARTEN   CULTURE. 


8l 


ingenious  as  it  is  simple.  The  same  course  as  pur- 
sued in  the  study  of  things,  according  to  their  form, 
size  and  number,  and  mathematical  proportions  is 
also  here  adhered  to.  The  various  forms  which  have 
previously  occupied  the  child  in  their  existence  as 
bodies,  appear  here  in  drawn  pictures,  and  are  multi- 
plied ad  infinitum.  The  progression  from  the  sim- 
plest rudiment  to  the  more  complicated,  the  great 
multiplicity  of  series,  determined  by  the  various  direc- 
tions of  the  lines  and  the  geometric  fundamental  forms 
the  logical  progression  from  the  straight  to  the  curved 
lines,  render  drawing — not  considering  here  its  im- 
mediate artistic  significance  —  one  of  the  most  ef- 
ficient means  for  disciplining  tl.e  mind  of  the  young 
pupil.  It  is  the  first  step  lor  the  child  to  a  future 
careful  observation  of  the  general  connection  of  things 
from  the  smallest  to  the  largest,  as  parts  as  well  as 
wholes. 

In  the  following  occupations,  the  material  of  which 
is  a  more  refined  one,  color  is  introduced  in  connec- 
tion with  multiplication  of  form,  and  the. products  of 
the  children's  work  are  constantly  approaching  real 
artistic  creations.  In  the  braiding,  or  loeaving  the 
thought  of  number  is  predominating  because  the  op- 
posites  of  odd  and  even  are  combined  by  alternately 
employing  both.  In  the  paper-folding,  opposites  are 
formed  by  the  oppositional  directions  of  the  lines, 
(horizontal  or  perpendicular)  originating  in  the  folding 
of  the  paper,  and  these  opposites  are  connected  by 
the  mediative  oblique  line.  In  like  manner  this  law 
is  applied  to  angles,  acute  and  obtuse  as  opposites, 
the  right  angle  serving  as  a  mediatory.  This  is  re- 
peated in  the  occupation  oi  perforating  3X\d  embroider- 
ing. The  cutting  of  paper,  also,  especially  affords  a 
perfect  view  of  all  the  mathematical  elements  for  the 
purpose  of  plastic  representation. 

Thus  we  find  everywhere  the  same  logical  chain  of 
perception,  and  subsequent  representation  and  exper- 
imental knowledge  resulting  from  both,  and  tlius  all 
parts  and  sections  of  this  s-ystem  of  occupation  are 
logically  united  with  one  another,  serving  the  child's 
mind  as  a  faithful  reflector  of  its  own  internal  devel- 
opment at  each  and  every  step.  And  well  may  the 
matured  mind,  developed  according  to  these  princi- 
ples, in  future  days  retrace  with  facility  its  conceiving 
and  thinking  to  the  clear  and  sharply  defined,  as  it 
were,  typical  images  of  this  reflector,  as  their  very 
origin,  for  such  experiences  surely  can  never  be  ef- 
faced. 

It  has  been  charged  by  those  who  have  only  a  su- 
perficial knowledge  of  Froebel's  educational  system, 
\  that  by  it  the  faculties  of  the  young  mjnd  are  too 
soon  awakened,  which  should  not  be  taxed  at  so 
early  an  age.  To  this  accusation  we  invite  the  most 
careful   investigation,  the  result  of  which,  w-e  doubt 


not,  will  be  a  conviction  that  just  the  opposite  is  the 
case. 

Manual  occupation,  performed  in  connection  with 
ail  means  of  occupation  in  the  Kinder-Garten,  con- 
tinual representation  of  objects,  plastic  formation  and 
production,  are  all  attractive  to  the  nature  of  the  child 
and  touch  the  springs  of  spontaneity  in  its  very  core. 
All  observations  which  appeal  to  the  understanding 
and  prepare  mathematical  conceptions  occur,  as  it 
were,  as  accessories  only,  and  to  such  an  extent  as  the 
child's  desire  calls  for  them.  Nothing  is  ever  forced 
upon  the  pupil's  mind.  It  can  not  even  be  said  that 
teaching  is  prominent,  but  rather  practical  occupation, 
individually-intended  production,  on  the  part  of  the 
children ;  which  give  rise  to  most  of  the  remarks  re- 
quired to  be  made  on  the  part  of  the  Kinder-Gartner. 
The  element  of  zvorkiug,  w^hich  every  child's  nature 
craves,  is  predominating.  Activity  of  the  hand  is  the 
fundamental  conditioi>of  all  development  in  the  child, 
as  it  is  also  the  fundamental  condition  for  the  acquisi- 
tion of  knmuledge,  and  the  subjection  of  matter.  Me- 
chanical ability,  technical  dexterity,  education  of  all 
human  senses  require  under  all  circumstances  manual 
occupation.  However,  if  this  side  of  Froebel's  edu- ' 
cational  system  is  mentioned,  another  class  of  op- 
ponents is  ready  to  object,  that  the  child  should  not 
begin  with  work,  but  that  first  its  mind  should  be  de- 
veloped. We  understand  these  various  objections  to 
mean  that  the  child's  powers  should  not  be  employed 
in  mechanical  occupation  exclusively,  nor  be  entirely 
deprived  of  it,  but  that  a  harmonious  development  of 
body  and  mind  should  be  the  task  of  education.  This 
is  in  perfect  accordance  with  Froebel's  principles, 
which,  if  carried  out  rightly,  will  accomplish  this  in 
tl.e  fullest  meaning  of  the  word.  No  occupation  in 
the  Kinder-Garten  is  merely  mechanical,  it  is  one  of 
the  most  important  rules  that  the  mere  mechanical, 
as  contrary  to  the  child's  nature,  should  studiously  be 
avoided. 

Nothing  is  plainer  to  the  careful  observer  of  the 
child's  nature  than  the  desire  of  the  little  mind  to  ob- 
serve and  imbibe  (///its  surroundings  with  all  its  senses 
simultaneously.  It  wishes  to  see,  to  hear,  to  feel,  all 
beautiful,  joyful,  and  pleasant  things,  and  then  strives 
to  reproduce  them  as  far  as  its  limited  faculties  will 
admit.  To  receive  and  give  back,  is  life,  life  in  all  its 
directions,  with  all  its  powers  This  is  what  the  child 
desires,  what  it  should  be  led  to  accomplish  with  a 
view  to  its  own  development.  Eyes  and  ears  seek 
the  bea  tiful,  the  senses  of  taste  and  smell  enjoy  the 
agreeable,  and  the  impression  which  this  beautiful  and 
agreeable  make  upon  the  child's  mind  calls  forth  in 
the  child's  innermost  soul,  the  desire,  nay,  the  neces- 
sity of  production,  representation,  or  formation.  If 
we  should  neglect  providing  tiie  means  to  gratify  sach 


82 


KINDER-GARTEN    CULTURE. 


desire,  a  full  development  of  the  heart  of  the  individ- 
ual, a  higher  taste  for  the  ideal  in  it,  never  could  be 
the  result  We  believe  that  this  desire  can  not  be 
assisted  more  perfectly  and  appropriately  than  by  ac- 
complishment in  form,  color,  and  tone,  each  express- 
ing and  representing  in  its  own  manner,  the  feeling  of 
the  beautiful  and  agreeable.  The  earlier  such  accom- 
plishment is  begun,  the  more  perfectly  the  heart  or 
aesthetic  sentiment  in  man  will  be  developed,  the  more 
surely  a  foundation  for  the  moral  development  of  the 
individual  be  laid  Aptness  in  formation  and  produc- 
tion conditions  development  of  the  hand,  simultane- 
ously with  the  development  of  the  senses.  It  condi- 
tions,, also,  knowledge  and  subjection  of  matter  and 
the  proper  material  for  the  yet  weak  and  unskilled 
hand  of  children.  Formation  itself  furthermore  con- 
ditions observation  of  the  various  relations  of  form, 
size,  and  number,  as  shown  in  connection  with  the 
gifts,  employed  for  the  preparatory  development  of 
the  perceptive  faculties.  Mathematical  forms  and  fig- 
ures are,  as  it  were,  the  skeleton  of  the  beautiful  in 
form,  which,  in  its  perfection  always  requires  the 
curved  line.  Images  of  ancient  peoples,  as  we  find 
them  f.  i.  in  the  Egyptian  temples  are  straight-lined, 
hence  are  geometrical  figures.  The  curved  line,  the 
true  line  of  beauty,  we  find  subsequently,  when  the 
attistic  feeling  had  become  more  fully  developed. 
The  \oxvas,o{  beauty  alternating  in  ail  branches  of  Kin- 
der-Garten occupation,  with  those  of  life  and  knowl- 
edge, afford  the  most  appropriate  means  for  the  de- 
velopment of  a  sense  of  art  as  well  as  of  aptness  in 
art,  in  the  meantime  preventing  a  onesided  prevalence 
of  a  mere  cold  understanding. 

The  faculties  of  the  soul  are  not  yet  distinctly  sep- 
arated in  the  young  child,  the  understanding,  feeling 
and  will,  act  in  union  with  one  another  and  every  one 
is  developed  through  and  with  the  others.  The  com- 
binations of  the  power  of  representation  in  formation 
serve  also  as  the  preliminary  exercise  for  that  combi- 
nation of  thought ;  and  what  the  hand  produces 
strengthens  the  will  and  energy  of  the  young  mind  in 
the  meantime  affording  gratification  to  the  heart.  Ail 
work  of  man,  be  it  common  manual  work,  or  a  work 
of  art,  or  purely  mental  labor  is  always  the  uniting  of 
parts  to  a  whole,  /  e ,  organizing  in  the  highest  sense 
of  the  word.  The  more  we  are  conscious  of  aim, 
means,  manner  and  method  connected  with  our  work, 
the  more  the  mind  is  active  in  it,  the  higher  and  no- 
bler the  result  will  be.  The  lowest  step  of  human 
labor  is  formed  by  mechanical  imitation,  the  highest  is 
free  formation  or  production,  according  to  one's  own 
conception.  Between  these  two  points  we  find  the 
whole  scale  by  which  the  crudest  kind  of  labor  mounts 
to  a  free  production  in  art  and  science  and  on  which 
invention  stands  uppermost  as  the  gradual  triumphant 


result  from  simplest  imitation.  It  is  this  scale  en  min- 
iature through  which  the  child's  mind  is  conducted  by 
means  of  Froebel's  occupation  material.  P'rom  the 
first  immediate  impression,  received  from  objects  and 
forms  of  the  visible  world,  it  rises  to  art,  or  creation 
according  to  own  ideas,  which  is  its  own  production, 
a  self-willed  formation.  For  this  purpose  nature  im- 
planted in  the  human  mind  a  strong  desire  to  produce 
form,  which,  if  correctly  guided,  becomes  the  most 
useful  faculty  of  the  soul.  Simply  by  this  desire  of 
formation  the  images  of  perception  attain  the  neces- 
sary perfect  distinctness  and  clearness,  the  power  of 
observation,  its  keenness  and  experience,  its  proofs, 
all  of  which  are  requisite,  to  afford  to  the  working  of  the 
human  mind  a  sure  foundation.  Free  invention,  creat- 
ing, is  the  culminating  point  of  menial  independence. 
We  lead  the  child  to  this  eminence  by  degrees.  Some- 
times accident  has  led  to  invention  and  production  of 
thte  new,  but  Froebel  has  provided  a  systematically 
graded  method  by  which  infancy  may  at  once  start 
upon  the  rojd  to  this  eminent  aim  of  inventing. 

If  the  full  consciousness,  the  clear  conception  of  its 
aim  is  at  first  wanting,  it  is  prepared  by  every  step 
onward.  The  objects  presented,  and  the  material  em- 
jjloyed,  afford  the  child,  under  the  guidance  of  a  ma- 
ture mind,  the  alphabet  of  art,  as  well  as  that  of 
knowledge,  and  it  is  worth  while  here  to  remark  that 
history  shows  art  comes  before  science  in  all  humuu 
development. 

Tf  we  now  cast  a  retrospective  glance  upon  the 
means  of  occupation  in  the  Kinder-Garten,  we  find 
that  the  material  progressed  from  the  solid  and  whole  in 
gradual  steps  to  its  parts,  until  it  arrives  at  the  image 
.  upon  the  plane  and  its  conditions  as  to  line  and  point 
For  the  heavy  material,  fit  only  to  be  placed  upon  the 
table  in  unchanged  form  (the  building  blocks),  a  more 
flexible  one  is  substituted  in  the  following  occupations  : 
Wood  is  replaced  by  paper.  The  paper  plane  of  the 
folding  occupation,  is  replaced  by  the  paper  strip  of 
the  weaving  occupation,  as  line.  The  wooden  staff 
or  very  fine  wire  is  then  introduced  for  the  purpose  of 
executing  permanent  figures  in  connection  with  peas, 
representing  the  point.  In  place  of  this  material  the 
drawn  line  then  appears,  to  which  colors  are  added. 
Perforating  and  embroidering  introduces  another  ad- 
dition to  the  material  to  create  the  images  of  fantasy 
which,  in  the  paper- cutting  and  mounting,  again  re 
ceive  new  elements.  The  modeling  in  clay  or  wax 
affords  the  immediate  plastic  artistic  occupation,  with 
the  most  pliable  material  for  the  hand  of  the  child 
Song  introduces  into  the  realm  of  sound,  when  w«:'^- 
ment  plays,  gymnastics  and  dancing  help  to  educate  the 
body  and  insure  a  harmonious  development  of  all  its 
parts.  In  practicing  the  technical  manual  perform- 
ances of  the  mechanic,  such  as  boring,  piercing,  cut- 


KINDER-GARTEN   CULTURE. 


8 


ting,  measuring,  uniting,  forming,  drawing,  painting, 
and  modeling,  a  foundation  of  all  future  occupation  of 
artisan  and  artist — synonymous  in  classic  and  mediaeval 
antiquity — is  laid.  For  ornamentation,  especially,  all 
elements  are  found  in  the  occupations  of  the  Kin- 
der-Garten. The  forms  of  beauty  in  the  paper-fold- 
ing f  i.,  serve  as  series  of  rosettes  and  ornaments  in 
relief  that  architecture  might  employ  without  change. 
The  productions  in  the  braiding  department  contain 
all  conditions  of  artistic  weaving,  nor  does  the  cutting 
of  figures  fail  to  afford  richest  material  for  ornamen- 
tation of  various  kinds.  For  every  talent  in  man 
means  of  development  are  provided  in  the  Kinder- 
Garten  material.  Opportunity  for  practice  is  constantly 
given,  and  each  direction  of  the  mind  finds  its  starting- 
point  in  concrete  things.  No  more  complete  satis- 
faction, therefore,  can  be  given  to  the  claim  of  rational 
education  :  "that  all  ideas  should  be  founded  on  pre- 
vious perception,  derived  from  real  objects,"  than  is 
done  in  the  genuine  Kinder-Garten.  Whosoever  has 
acquired  even  a  superficial  idea  only  of  the  significance 
of  Froebel's  means  of  occupation  in  the  Kinder-Gar- 
ten, will  be  ready  to  admit  that  the  ordinary  play- 
things of  children  are  not,  by  any  means,  as  regards 
their  usefulness,  to  be  compared  with  the  occupation 
material  in  the  Kinder  Garten.  That  the  former  in  a 
certain  degree,  may  be  made  helpful  in  the  develop- 
ment of  children,  is  not  denied.  Occasional  good  re- 
sults with  them,  which,  however,  usually  will  be 
found  to  be  owing  to  the  child's  own  instinct  rather 
than  to  the  nature  of  the  toy.  Planless  playing,  with- 
out guidance  and  supervision,  can  not  prepare  a  child 
for  the  earnest  sides  of  life,  or  even  for  the  enjoyment 
of  its  own  harmless  amusements  and  pleasures.  Like 
the  plant,  which,  even  in  the  wilderness,  draws  from 
the  soil  its  nutrition,  so  the  child's  mind  draws  from 
its  surroundings  and  the  means,  placed  at  its  com- 


mand, its  educational  food.  IJut  the  rose-bush, 
nursed  and  cared  for  in  the  garden  by  the  skillful  hor- 
ticulturist, produces  flowers  far  more  perfict  and 
beautiful  than  the  wild-growing  sweet-briar.  With- 
out care  neither  the  mind  nor  the  body  of  the  child 
can  be  expected  to  prosper.  As  the  latter  can  not, 
for  a  healthful  development,  use  all  kinds  of  food 
without  careful  selection,  so  the  mind  for  its  higher 
cultivation  requires  a  still  more  careful  choice  of  the 
means  for  its  development.  The  child's  free  choice  is 
limited  only  in  so  far  as  it  is  necessary  to  limit  the 
amount  of  occupation  mateiial  in  order  to  fit  it  for 
systematic  application  The  child  will  find,  instinct- 
ively, all  that  is  requisite  for  its  mental  growth,  if  the 
proper  material  only  be  presented,  and  a  guiding  mind 
indicate  its  most  appropriate  use  in  accordance  with  a 
certain  Inv. 

Froebel's  genius  has  admirably  succeeded  in  invent- 
ing the  proper  material  as  well  as  in  pointing  out  its 
most  successful  application,  to  prepare  the  child  for 
all  situations  in  future  life,  for  all  branches  of  occupa- 
tion in  the  useful  pursuits  of  mankind.  When  the 
Kinder-Garten  was  first  established  by  Froebel,  it  was 
prohibited,  and  its  inventor  driven  from  place  to  place 
in  his  fatherland  on  account  of  his  liberal  educational 
principles  to  be  carried  out  in  the  Kinder-Garien. 
The  keen  eye  of  monarchial  government  officials 
quickly  saw  that  such  institution  would  not  turn  out 
passive  subjects  to  tyrannical  oppression  and  the 
rulers  "^y  ^he  grace  of  God''''  tolerated  the  Kinder- 
Garten  only  when  public  opinion  declared  too  strongly 
in  its  favor  to  be  safely  resisted.  In  pleading  the 
cause  of  the  Kinder-Garten  on  the  soil  of  republican 
America,  do  I  ask  too  much  if  I  invite  all  to  assist 
in  extending  to  future  generations  the  benefits  to  be. 
derived  from  an  institution  so  eminently  fit  to  educate 
free  citizens  of  a  free  country  ? 


APPENDIX  TO  CHAPTER  ON  PERFORATING  AND 

EMBROIDERY. 

(Page  55.) 


Since  the  publication  of  the  foregoing 
pages  a  considerable  advance  has  been  made 
in  the  occupation  of  embroidery,  and  the 
publishers  take  the  liberty  to  make  a  few 
statements  which  they  believe  to  be  accepted 
facts,  but  for  which  the  author  of  the  book  is 
in  no  way  responsible. 

Owing  to  the  tax  on  the  eyes,  the  perforat- 
ing occupation  has  been  deemed  by  many 
as  rather  undesirable  if  carried  to  any  consid- 
erable extent,  and  hence  it  is  not  thought 
wise  to  require  the  child  to  perforate  the  ele- 
mentary patterns  for  embroidery.  But  this 
work,  if  thrown  upon  the  teacher,  would  be 
too  heavy  a  task  and  a  useless  waste  of  energy, 
as  the  patterns  can  be  so  much  more  rapidly 
pricked  by  machinery. 

Therefore  Bradley's  Pricked  Cards  were 
devised  many  years  ago,  the  designs  for  which 
were  based  on  the  German  school  of  em- 
broidery. More  recently  American  Kinder- 
gartners  have  materially  abridged  the  number 
of  designs  to  be  used  in  the  course,  and  sev- 
eral years  ago  the  ladies  of  the  Florence 
Kindergarten  made  the  selection  illustrated 
in  Plate  La,  which  was  styled  the  Florence 
School  of  Sewing.  This  course  has  given 
good  satisfaction  to  a  large  number  of  Kinder- 
gartners  who  have  adopted  it.  But  as  every 
thoughtful  Kindergartner  has  her  own  ideas, 
suggestions  for  changes  have  been  made  from 
time  to  time,  and  a  ucmv  arrangement  illus- 
trated in  Plate  Lb  is  the  result  of  the  confer- 
ence of  several  experienced  Kindergartners, 
and  is  christened  the  Winona  School  of 
Sewing. 

After  vertical   and  horizontal  lines,   their 


combination  into  right  angles,  squares  and 
oblongs  follows,  and  the  oblique  line  is  not 
introduced  even  indirectly  until  the  seventh 
card. 

The  diagonals  of  squares,  singly  and  com- 
bined, follow  in  the  ne.xt  six  cards,  and  the 
diagonals  of  vertical  and  horizontal  oblongs, 
combined  in  the  same  order,  fill  the  next 
twelve,  some  new  designs  having  been  made 
to  complete  the  series. 

The  rhombus  follows  naturally  the  diago- 
nals of  oblongs. 

This  course  gives  children  who  are  suffi- 
ciently advanced  an  opportunity  to  invent, 
which  can  be  easily  done  on  cards  pricked 
regularly  in  squares. 

The  entire  series  of  cards  comprises  more 
than  fifty  different  patterns  of  sewing,  although 
in  several  instances  the  same  pattern  of  prick- 
ing serves  for  more  than  one  pattern  of  sew- 
ing. There  are  also  cards  pricked  in  regu- 
lar squares  over  the  entire  surface  except  a 
margin.  All  the  pattern-cards  are  on  white 
cardboard,  the  contrasts  being  secured  in  the 
colors  of  the  worsteds,  but  the  regularly  per- 
forated are  in  tints  as  well  as  white.  The 
pattern-cards  are  3|x4|  inches.  The  others 
in  several  sizes. 

Cards  with  outlines  of  natural  objects  for 
embroidery  have  long  been  in  use,  and  are 
considered  very  desirable.  A  series  of  origi- 
nal designs  is  now  offered,  embracing  ani- 
mals, flowers,  figures  of  children,  and  Christ- 
mas and  New  Year's  cards. 

A  complete  illustrated  list  of  all  the  above 
cards  sent  to  any  address  on  application  to 
the  publishers  of  this  book. 


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